Slider-Crank DAE Work-Precision Diagrams
This is a benchmark of the Slider-Crank mechanism with elastic connecting rod, an index-2 DAE of dimension 24 from the IVP Test Set (Simeon 1998, crank.f).
The system models a crank-rod-slider mechanism where the connecting rod is treated as a flexible beam with 4 finite-element modes (2 lateral, 2 axial). The crank angle is prescribed as φ₁(t) = Ωt with Ω = 150 rad/s.
Variables (17 state variables):
- 7 positions: φ₁, φ₂, x₃, q₁, q₂, q₃, q₄
- 7 velocities: v₁, v₂, vx₃, vq₁, vq₂, vq₃, vq₄
- 3 Lagrange multipliers: λ₁, λ₂, λ₃
We benchmark three formulations of this problem:
- DAE Residual Form:
F(du, u, t) = M·du − f(u, t) = 0, solved with dedicated DAE solvers (IDA from Sundials). - MTK Index-Reduced ODE: The system defined symbolically with position-level constraints, automatically index-reduced by
structural_simplifyto a 13-state ODE. - Mass-Matrix ODE Form:
M·du/dt = f(u, t), solved with ODE solvers that handle singular mass matrices (Rosenbrock-W methods, multistep BDF).
The mass matrix is frozen at t = 0, which limits achievable tolerance to around 1e-7.
Reference: Simeon, B.: Modelling a flexible slider crank mechanism by a mixed system of DAEs and PDEs, Math. Modelling of Systems 2, 1-18 (1996).
using OrdinaryDiffEq, Sundials, DiffEqDevTools, ModelingToolkit, Plots
using LinearAlgebra
using ModelingToolkit: t_nounits as t, D_nounits as D
# ── Physical Parameters (from crank.f) ──────────────────────────────
const M1 = 0.36
const M2 = 0.151104
const M3 = 0.075552
const L1 = 0.15
const L2 = 0.30
const J1 = 0.002727
const J2 = 0.0045339259
const PI_ = 3.1415927
const EE = 0.20e12
const NUE = 0.30
const BB = 0.0080
const HH = 0.0080
const RHO = 7870.0
const GRAV = 0.0
const OMEGA = 150.0
const NQ = 4
const NP = 7
const NL = 3
const KU = 4
const KV = 0
# ── FE Matrices (exact port of FIRST block in RESMBS) ───────────────
function initialize_fe_matrices()
FACM = RHO * BB * HH * L2
FACK = EE * BB * HH / L2
FACB = BB * HH * L2
MQ_ = zeros(NQ, NQ)
MQ_[1,1] = FACM * 0.5
MQ_[2,2] = FACM * 0.5
MQ_[3,3] = FACM * 8.0
MQ_[3,4] = FACM * 1.0
MQ_[4,3] = FACM * 1.0
MQ_[4,4] = FACM * 2.0
KQ_ = zeros(NQ, NQ)
KQ_[1,1] = FACK * PI_^4 / 24.0 * (HH/L2)^2
KQ_[2,2] = FACK * PI_^4 * 2.0 / 3.0 * (HH/L2)^2
KQ_[3,3] = FACK * 16.0 / 3.0
KQ_[3,4] = -FACK * 8.0 / 3.0
KQ_[4,3] = -FACK * 8.0 / 3.0
KQ_[4,4] = FACK * 7.0 / 3.0
BQ_ = zeros(NQ, NQ)
BQ_[1,3] = -FACB * 16.0 / PI_^3
BQ_[1,4] = FACB * (8.0 / PI_^3 - 1.0 / PI_)
BQ_[2,4] = FACB * 0.5 / PI_
BQ_[3,1] = FACB * 16.0 / PI_^3
BQ_[4,1] = -FACB * (8.0 / PI_^3 - 1.0 / PI_)
BQ_[4,2] = -FACB * 0.5 / PI_
DQ_ = zeros(NQ, NQ)
c1_ = zeros(NQ); c2_ = zeros(NQ)
c12_ = zeros(NQ); c21_ = zeros(NQ)
c1_[3] = FACB * 2.0 / 3.0
c1_[4] = FACB * 1.0 / 6.0
c2_[1] = FACB * 2.0 / PI_
c12_[3] = L2 * FACB * 1.0 / 3.0
c12_[4] = L2 * FACB * 1.0 / 6.0
c21_[1] = L2 * FACB * 1.0 / PI_
c21_[2] = -L2 * FACB * 0.5 / PI_
return MQ_, KQ_, BQ_, DQ_, c1_, c2_, c12_, c21_
end
const MQ, KQ, BQ, DQ, c1, c2, c12, c21 = initialize_fe_matrices()([0.075552 0.0 0.0 0.0; 0.0 0.075552 0.0 0.0; 0.0 0.0 1.208832 0.151104; 0.
0 0.0 0.151104 0.302208], [123144.33964567189 0.0 0.0 0.0; 0.0 1.9703094343
307503e6 0.0 0.0; 0.0 0.0 2.2755555555555558e8 -1.1377777777777779e8; 0.0 0
.0 -1.1377777777777779e8 9.955555555555557e7], [0.0 0.0 -9.90767093878593e-
6 -1.1577142550509449e-6; 0.0 0.0 0.0 3.055774862221955e-6; 9.9076709387859
3e-6 0.0 0.0 0.0; 1.1577142550509449e-6 -3.055774862221955e-6 0.0 0.0], [0.
0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0], [0.0, 0.
0, 1.28e-5, 3.2e-6], [1.222309944888782e-5, 0.0, 0.0, 0.0], [0.0, 0.0, 1.92
e-6, 9.6e-7], [1.833464917333173e-6, -9.167324586665865e-7, 0.0, 0.0])Consistent Initial Conditions
The Fortran reference code (init1 in crank.f) provides positions and velocities. We ensure full consistency by:
- Using init1 positions (which satisfy the position-level constraints).
- Projecting init1 velocities onto the constraint manifold via minimum-norm correction.
- Computing consistent accelerations and Lagrange multipliers by solving the augmented saddle-point system
[AM GP'; GP 0] * [w; λ] = [F; γ].
function build_GP(p1, p2, q)
cosp1 = cos(p1); sinp1 = sin(p1)
cosp2 = cos(p2); sinp2 = sin(p2)
qku = (KU == 0) ? 0.0 : q[KU]
qkv = (KV == 0) ? 0.0 : q[KV]
GP = zeros(3, NP)
GP[1,1] = L1 * cosp1
GP[1,2] = L2 * cosp2 + qku * cosp2 - qkv * sinp2
GP[2,1] = L1 * sinp1
GP[2,2] = L2 * sinp2 + qku * sinp2 + qkv * cosp2
GP[2,3] = 1.0
GP[3,1] = 1.0
if KU != 0
GP[1, 3+KU] = sinp2
GP[2, 3+KU] = -cosp2
end
return GP
end
function build_AM(p1, p2, q)
cosp12 = cos(p1 - p2); sinp12 = sin(p1 - p2)
c1Tq = dot(c1, q); c2Tq = dot(c2, q)
c12Tq = dot(c12, q); qtmqq = dot(q, MQ * q)
QtBQ = zeros(NQ)
for i in 1:NQ
QtBQ[i] = dot(q, @view BQ[:, i])
end
AM = zeros(NP, NP)
AM[1,1] = J1 + M2 * L1^2
AM[1,2] = 0.5 * L1 * L2 * M2 * cosp12 +
RHO * L1 * (sinp12 * c2Tq + cosp12 * c1Tq)
AM[2,2] = J2 + qtmqq + 2.0 * RHO * c12Tq
AM[3,3] = M3
for i in 1:NQ
AM[1, 3+i] = RHO * L1 * (-sinp12 * c1[i] + cosp12 * c2[i])
AM[2, 3+i] = RHO * c21[i] + RHO * QtBQ[i]
end
for i in 1:NQ, j in 1:i
AM[3+j, 3+i] = MQ[j, i]
end
for i in 1:NP, j in i+1:NP
AM[j, i] = AM[i, j]
end
return AM
end
function compute_force_vector(p1, p2, q, v1, v2, vq)
cosp12 = cos(p1 - p2); sinp12 = sin(p1 - p2)
cosp1 = cos(p1); sinp1 = sin(p1)
cosp2 = cos(p2); sinp2 = sin(p2)
c1Tq = dot(c1, q); c1Tqd = dot(c1, vq)
c2Tq = dot(c2, q); c2Tqd = dot(c2, vq)
c12Tqd = dot(c12, vq)
MQq = MQ * q; KQq = KQ * q; DQqd = DQ * vq; BQqd = BQ * vq
qdtmqq = dot(vq, MQq); qdtbqqd = dot(vq, BQqd)
F = zeros(NP)
F[1] = -0.5 * L1 * GRAV * (M1 + 2.0 * M2) * cosp1 -
0.5 * L1 * L2 * M2 * v2^2 * sinp12
F[2] = -0.5 * L2 * GRAV * M2 * cosp2 +
0.5 * L1 * L2 * M2 * v1^2 * sinp12
F[3] = 0.0
F[1] += RHO * L1 * v2^2 * (-sinp12 * c1Tq + cosp12 * c2Tq) -
2.0 * RHO * L1 * v2 * (cosp12 * c1Tqd + sinp12 * c2Tqd)
F[2] += RHO * L1 * v1^2 * (sinp12 * c1Tq - cosp12 * c2Tq) -
2.0 * RHO * v2 * c12Tqd - 2.0 * v2 * qdtmqq -
RHO * qdtbqqd - RHO * GRAV * (cosp2 * c1Tq - sinp2 * c2Tq)
for i in 1:NQ
F[3+i] = v2^2 * MQq[i] +
RHO * (v2^2 * c12[i] + L1 * v1^2 * (cosp12 * c1[i] + sinp12 * c2[i]) +
2.0 * v2 * BQqd[i]) -
RHO * GRAV * (sinp2 * c1[i] + cosp2 * c2[i])
F[3+i] -= KQq[i] + DQqd[i]
end
return F
end
function get_consistent_ic()
# Step 1: Positions from init1 (satisfy position constraints)
p1 = 0.0; p2 = 0.0; x3 = 0.450016933
q = [0.0, 0.0, 0.103339863e-04, 0.169327969e-04]
pos = [p1, p2, x3, q...]
# Step 2: Project init1 velocities onto constraint manifold
v_init1 = [150.0, -74.9957670, -0.268938672e-05,
0.444896105, 0.463434311e-02,
-0.178591076e-05, -0.268938672e-05]
GP0 = build_GP(p1, p2, q)
target = [0.0, 0.0, OMEGA]
residual_v = GP0 * v_init1 - target
v_fixed = v_init1 - GP0' * ((GP0 * GP0') \ residual_v)
# Step 3: Compute accelerations and multipliers
AM0 = build_AM(p1, p2, q)
F0 = compute_force_vector(p1, p2, q, v_fixed[1], v_fixed[2], v_fixed[4:7])
# dGP/dt * v via finite differences
eps_fd = 1e-8
pos_p = pos .+ eps_fd .* v_fixed
GP_p = build_GP(pos_p[1], pos_p[2], pos_p[4:7])
dGPdt_v = (GP_p - GP0) / eps_fd * v_fixed
# Augmented saddle-point system: [AM GP'; GP 0] [w; λ] = [F; -dGP/dt*v]
n = NP + NL
Aug = zeros(n, n)
Aug[1:NP, 1:NP] = AM0
Aug[1:NP, NP+1:n] = GP0'
Aug[NP+1:n, 1:NP] = GP0
rhs = zeros(n)
rhs[1:NP] = F0
rhs[NP+1:n] = -dGPdt_v
sol = Aug \ rhs
w_0 = sol[1:NP]
lam_0 = sol[NP+1:n]
return pos, v_fixed, w_0, lam_0, AM0, GP0
end
pos0, vel0, w0, lam0, AM0, GP0 = get_consistent_ic()
# Verify constraints
g1 = L1 * sin(pos0[1]) + (L2 + pos0[7]) * sin(pos0[2])
g2 = pos0[3] - L1 * cos(pos0[1]) - (L2 + pos0[7]) * cos(pos0[2])
g3 = pos0[1]
println("Position constraints: ", [g1, g2, g3])
println("Velocity constraint norm: ", norm(GP0 * vel0 - [0, 0, OMEGA]))Position constraints: [0.0, 2.0309998127743256e-10, 0.0]
Velocity constraint norm: 0.0Mass-Matrix ODE Formulation
The index-2 DAE is reformulated as a singular mass-matrix ODE with 17 state variables u = [p; v; λ]. The mass matrix M has the structure:
M = [I 0 0 ] du = [v ]
[0 AM 0 ] [F - Gᵀλ ]
[0 0 0 ] [G*v - r'(t) ]where AM is the 7×7 generalized mass matrix (frozen at t=0) and G is the 3×7 constraint Jacobian (evaluated at current state).
function slider_crank_mm!(du, u, p, t)
T = eltype(u)
p1, p2, x3 = u[1], u[2], u[3]
q = @view u[4:7]
v1, v2 = u[8], u[9]
vq = @view u[11:14]
lam1, lam2, lam3 = u[15], u[16], u[17]
cosp1 = cos(p1); sinp1 = sin(p1)
cosp2 = cos(p2); sinp2 = sin(p2)
cosp12 = cos(p1 - p2); sinp12 = sin(p1 - p2)
qku = (KU == 0) ? zero(T) : q[KU]
qkv = (KV == 0) ? zero(T) : q[KV]
c1Tq = dot(c1, q); c1Tqd = dot(c1, vq)
c2Tq = dot(c2, q); c2Tqd = dot(c2, vq)
c12Tqd = dot(c12, vq)
MQq = MQ * q; KQq = KQ * q
DQqd = DQ * vq; BQqd = BQ * vq
qtmqq = dot(q, MQq)
qdtmqq = dot(vq, MQq)
qdtbqqd = dot(vq, BQqd)
QtBQ = zeros(T, NQ)
for i in 1:NQ
QtBQ[i] = dot(q, @view BQ[:, i])
end
# Constraint Jacobian GP (3×7) — evaluated at current state
GP = zeros(T, 3, NP)
GP[1,1] = L1 * cosp1
GP[1,2] = L2 * cosp2 + qku * cosp2 - qkv * sinp2
GP[2,1] = L1 * sinp1
GP[2,2] = L2 * sinp2 + qku * sinp2 + qkv * cosp2
GP[2,3] = one(T)
GP[3,1] = one(T)
if KU != 0
GP[1, 3+KU] = sinp2
GP[2, 3+KU] = -cosp2
end
# Force vector F (7)
F = zeros(T, NP)
F[1] = -0.5 * L1 * GRAV * (M1 + 2.0 * M2) * cosp1 -
0.5 * L1 * L2 * M2 * v2^2 * sinp12
F[2] = -0.5 * L2 * GRAV * M2 * cosp2 +
0.5 * L1 * L2 * M2 * v1^2 * sinp12
F[3] = zero(T)
F[1] += RHO * L1 * v2^2 * (-sinp12 * c1Tq + cosp12 * c2Tq) -
2.0 * RHO * L1 * v2 * (cosp12 * c1Tqd + sinp12 * c2Tqd)
F[2] += RHO * L1 * v1^2 * (sinp12 * c1Tq - cosp12 * c2Tq) -
2.0 * RHO * v2 * c12Tqd - 2.0 * v2 * qdtmqq -
RHO * qdtbqqd - RHO * GRAV * (cosp2 * c1Tq - sinp2 * c2Tq)
for i in 1:NQ
F[3+i] = v2^2 * MQq[i] +
RHO * (v2^2 * c12[i] + L1 * v1^2 * (cosp12 * c1[i] + sinp12 * c2[i]) +
2.0 * v2 * BQqd[i]) -
RHO * GRAV * (sinp2 * c1[i] + cosp2 * c2[i])
F[3+i] -= KQq[i] + DQqd[i]
end
# Block 1 (rows 1:7): I * dp/dt = v
for i in 1:7
du[i] = u[7+i]
end
# Block 2 (rows 8:14): AM * dv/dt = F - Gᵀλ
for i in 1:NP
du[7+i] = F[i] - GP[1,i] * lam1 - GP[2,i] * lam2 - GP[3,i] * lam3
end
# Block 3 (rows 15:17): 0 * dλ/dt = G*v - r'(t)
for k in 1:3
vlc = zero(T)
for i in 1:NP
vlc += GP[k, i] * u[NP+i]
end
if k == 3
vlc -= OMEGA
end
du[14+k] = vlc
end
nothing
end
function build_mass_matrix(AM)
Mfull = zeros(17, 17)
for i in 1:7
Mfull[i, i] = 1.0 # identity block for dp/dt = v
end
Mfull[8:14, 8:14] .= AM # AM block for dv/dt equations
# rows 15:17 are zero → algebraic (velocity constraints)
return Mfull
end
u0_mm = vcat(pos0, vel0, lam0)
M_mm = build_mass_matrix(AM0)
mmf = ODEFunction(slider_crank_mm!, mass_matrix = M_mm)
tspan = (0.0, 0.1)
prob_mm = ODEProblem(mmf, u0_mm, tspan)ODEProblem with uType Vector{Float64} and tType Float64. In-place: true
Non-trivial mass matrix: true
timespan: (0.0, 0.1)
u0: 17-element Vector{Float64}:
0.0
0.0
0.450016933
0.0
0.0
1.03339863e-5
1.69327969e-5
150.0
-74.99576703969453
-2.68938672e-6
0.444896105
0.00463434311
-1.78591076e-6
-2.68938672e-6
-2.303851027879405e-5
382.45895095266985
-6.339193797155536e-7DAE Residual Form
The same system can be written as a DAE residual F(du, u, t) = M·du − f(u, t) = 0, where M is the mass matrix and f is the right-hand side from the ODE form. This enables testing DAE-specific solvers like IDA (Sundials) and comparing how formulation choice affects solver performance.
function slider_crank_dae!(res, du, u, p, t)
f = similar(u)
slider_crank_mm!(f, u, p, t)
res .= M_mm * du - f
nothing
end
du0_dae = vcat(vel0, w0, zeros(3))
differential_vars = [trues(14); falses(3)]
prob_dae = DAEProblem(slider_crank_dae!, du0_dae, u0_mm, tspan,
differential_vars = differential_vars)
# Verify DAE consistency at initial conditions
f_check = similar(u0_mm)
slider_crank_mm!(f_check, u0_mm, nothing, 0.0)
println("DAE residual norm at IC: ", norm(M_mm * du0_dae - f_check))DAE residual norm at IC: 6.940448042111208e-15MTK Index-Reduced Formulation
ModelingToolkit can automatically reduce the DAE index via structural_simplify. We define the full system symbolically — with the 7 kinematic equations, 7 dynamics equations (involving the configuration-dependent mass matrix), and the 3 position-level holonomic constraints — and let MTK differentiate and eliminate the Lagrange multipliers, producing a 13-state ODE.
@variables begin
φ1(t) = pos0[1]
φ2(t) = pos0[2]
x₃(t) = pos0[3]
q₁(t) = pos0[4]
q₂(t) = pos0[5]
q₃(t) = pos0[6]
q₄(t) = pos0[7]
vφ1(t) = vel0[1]
vφ2(t) = vel0[2]
vx₃(t) = vel0[3]
vq₁(t) = vel0[4]
vq₂(t) = vel0[5]
vq₃(t) = vel0[6]
vq₄(t) = vel0[7]
λ₁(t) = lam0[1]
λ₂(t) = lam0[2]
λ₃(t) = lam0[3]
end
pvec = [φ1, φ2, x₃, q₁, q₂, q₃, q₄]
vvec = [vφ1, vφ2, vx₃, vq₁, vq₂, vq₃, vq₄]
qvec = [q₁, q₂, q₃, q₄]
vqvec = [vq₁, vq₂, vq₃, vq₄]
λvec = [λ₁, λ₂, λ₃]
# Symbolic trigonometric quantities
sφ1 = sin(φ1); cφ1 = cos(φ1)
sφ2 = sin(φ2); cφ2 = cos(φ2)
sφ12 = sin(φ1 - φ2); cφ12 = cos(φ1 - φ2)
# Dot products with FE vectors (Float64 constants × symbolic variables)
c1q = sum(c1 .* qvec); c2q = sum(c2 .* qvec); c12q = sum(c12 .* qvec)
c1vq = sum(c1 .* vqvec); c2vq = sum(c2 .* vqvec); c12vq = sum(c12 .* vqvec)
# Matrix-vector products (Float64 FE matrices × symbolic vectors)
MQq_s = MQ * qvec; KQq_s = KQ * qvec
DQvq_s = DQ * vqvec; BQvq_s = BQ * vqvec
# Quadratic forms
qMQq_s = sum(qvec .* MQq_s)
vqMQq_s = sum(vqvec .* MQq_s)
vqBQvq_s = sum(vqvec .* BQvq_s)
QBQ_s = [sum(qvec .* BQ[:,i]) for i in 1:NQ]
# AM(φ,q) × D(v) — configuration-dependent mass matrix × acceleration
am_dv = [
(J1 + M2*L1^2)*D(vφ1) +
(0.5*L1*L2*M2*cφ12 + RHO*L1*(sφ12*c2q + cφ12*c1q))*D(vφ2) +
sum(RHO*L1*(-sφ12*c1[i] + cφ12*c2[i])*D(vqvec[i]) for i in 1:NQ),
(0.5*L1*L2*M2*cφ12 + RHO*L1*(sφ12*c2q + cφ12*c1q))*D(vφ1) +
(J2 + qMQq_s + 2*RHO*c12q)*D(vφ2) +
sum((RHO*c21[i] + RHO*QBQ_s[i])*D(vqvec[i]) for i in 1:NQ),
M3*D(vx₃),
[RHO*L1*(-sφ12*c1[k] + cφ12*c2[k])*D(vφ1) +
(RHO*c21[k] + RHO*QBQ_s[k])*D(vφ2) +
sum(MQ[k,j]*D(vqvec[j]) for j in 1:NQ)
for k in 1:NQ]...
]
# Force vector F(φ,v,q,vq)
F_s = [
-0.5*L1*GRAV*(M1+2*M2)*cφ1 - 0.5*L1*L2*M2*vφ2^2*sφ12 +
RHO*L1*vφ2^2*(-sφ12*c1q + cφ12*c2q) -
2*RHO*L1*vφ2*(cφ12*c1vq + sφ12*c2vq),
-0.5*L2*GRAV*M2*cφ2 + 0.5*L1*L2*M2*vφ1^2*sφ12 +
RHO*L1*vφ1^2*(sφ12*c1q - cφ12*c2q) -
2*RHO*vφ2*c12vq - 2*vφ2*vqMQq_s - RHO*vqBQvq_s -
RHO*GRAV*(cφ2*c1q - sφ2*c2q),
0,
[vφ2^2*MQq_s[i] + RHO*(vφ2^2*c12[i] +
L1*vφ1^2*(cφ12*c1[i] + sφ12*c2[i]) + 2*vφ2*BQvq_s[i]) -
RHO*GRAV*(sφ2*c1[i] + cφ2*c2[i]) - KQq_s[i] - DQvq_s[i]
for i in 1:NQ]...
]
# Constraint Jacobian GP(φ,q) and GP' × λ
GP_rows = [
[L1*cφ1, (L2+q₄)*cφ2, 0, 0, 0, 0, sφ2],
[L1*sφ1, (L2+q₄)*sφ2, 1, 0, 0, 0, -cφ2],
[1, 0, 0, 0, 0, 0, 0 ]
]
GPt_λ = [sum(GP_rows[k][i]*λvec[k] for k in 1:3) for i in 1:NP]
# 17 equations: 7 kinematic + 7 dynamics + 3 holonomic constraints
eqs = vcat(
[D(pvec[i]) ~ vvec[i] for i in 1:NP],
[am_dv[i] ~ F_s[i] - GPt_λ[i] for i in 1:NP],
[0 ~ L1*sφ1 + (L2 + q₄)*sφ2,
0 ~ x₃ - L1*cφ1 - (L2 + q₄)*cφ2,
0 ~ φ1 - OMEGA*t]
)
@mtkbuild sys = ODESystem(eqs, t)
prob_mtk = ODEProblem(sys, [], tspan; warn_initialize_determined = false)
println("MTK index-reduced: $(length(ModelingToolkit.unknowns(sys))) states ",
"(from 17 original)")MTK index-reduced: 13 states (from 17 original)Reference Solution
We compute a high-accuracy reference solution using Rodas5P at moderate tolerance. The frozen mass matrix limits how tight we can push tolerances before instability sets in, so reltol = abstol = 1e-6 provides the best balance of accuracy and stability for this problem.
ref_sol = solve(prob_mm, Rodas5P(), reltol = 1e-6, abstol = 1e-6,
maxiters = 10_000_000);
println("Reference solution: retcode = $(ref_sol.retcode), ",
"npoints = $(length(ref_sol.t)), t_final = $(ref_sol.t[end])")
mtk_ref = solve(prob_mtk, Rodas5P(), reltol = 1e-5, abstol = 1e-5,
maxiters = 10_000_000);
println("MTK reference: retcode = $(mtk_ref.retcode), ",
"npoints = $(length(mtk_ref.t)), t_final = $(mtk_ref.t[end])")Reference solution: retcode = Success, npoints = 11178, t_final = 0.1
MTK reference: retcode = Success, npoints = 3621, t_final = 0.1plot(ref_sol, idxs = [2, 3], title = "φ₂ and x₃",
xlabel = "t", ylabel = "value", lw = 2)
plot(ref_sol, idxs = [4, 5], title = "Lateral Elastic Modes q₁, q₂",
xlabel = "t", ylabel = "amplitude", lw = 2)
plot(ref_sol, idxs = [6, 7], title = "Axial Elastic Modes q₃, q₄",
xlabel = "t", ylabel = "amplitude", lw = 2)
plot(ref_sol, idxs = [15, 16, 17], title = "Lagrange Multipliers λ₁, λ₂, λ₃",
xlabel = "t", ylabel = "force", lw = 2)
DAE vs Mass-Matrix: Solver Performance
A key question for this benchmark is how problem formulation affects solver performance. We test DAE-specific solvers on the residual form.
println("=== DAE Solver Results ===")
println("Testing IDA (Sundials) on DAE residual form:")
try
dae_sol = solve(prob_dae, IDA(), reltol = 1e-4, abstol = 1e-4)
println(" IDA result: retcode = $(dae_sol.retcode), t_final = $(dae_sol.t[end])")
catch e
println(" IDA failed: $(typeof(e))")
end
println("\nTesting IDA with modified initialization:")
try
dae_sol2 = solve(prob_dae, IDA(init_all = false), reltol = 1e-4, abstol = 1e-4)
println(" IDA (init_all=false): retcode = $(dae_sol2.retcode), t_final = $(dae_sol2.t[end])")
catch e
println(" IDA (init_all=false) failed: $(typeof(e))")
end=== DAE Solver Results ===
Testing IDA (Sundials) on DAE residual form:
IDA result: retcode = Unstable, t_final = 0.0002465164025475332
Testing IDA with modified initialization:
IDA (init_all=false): retcode = Unstable, t_final = 0.0002465164025475332IDA fails with ConvergenceFailure at the first step on this problem, even with fully consistent initial conditions (DAE residual norm ≈ 7×10⁻²¹). The extreme stiffness from the elastic modulus (E = 2×10¹¹ Pa) causes the Newton solver to diverge, with step size collapsing to h ≈ 10⁻¹⁷. DASKR and DASSL exhibit the same failure mode.
This demonstrates that formulation choice critically affects solver performance for this problem: the mass-matrix ODE form avoids DAE solver difficulties by letting Rosenbrock-W methods handle the algebraic constraints through the singular mass matrix structure.
Work-Precision Diagrams
We compare solvers across all three formulations using WorkPrecisionSet with prob_choice to overlay DAE, MTK, and mass-matrix results on the same plot. IDA operates on the DAE residual form, the MTK index-reduced form is solved with Rosenbrock-W methods, and the mass-matrix ODE form uses Rosenbrock-W and BDF methods. The tolerance range is limited by the frozen mass matrix (instability above ~1e-7). The MTK form's overdetermined initialization system limits it to tolerances above ~1e-5.
probs = [prob_dae, prob_mtk, prob_mm]
refs = [ref_sol, mtk_ref, ref_sol]3-element Vector{SciMLBase.ODESolution{Float64, 2, Vector{Vector{Float64}},
Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{Float64}}}, Nothin
g, P, A, IType, SciMLBase.DEStats, Nothing, Nothing, Nothing, Nothing} wher
e {P, A, IType}}:
SciMLBase.ODESolution{Float64, 2, Vector{Vector{Float64}}, Nothing, Nothin
g, Vector{Float64}, Vector{Vector{Vector{Float64}}}, Nothing, SciMLBase.ODE
Problem{Vector{Float64}, Tuple{Float64, Float64}, true, SciMLBase.NullParam
eters, SciMLBase.ODEFunction{true, SciMLBase.FullSpecialize, typeof(Main.va
r"##WeaveSandBox#225".slider_crank_mm!), Matrix{Float64}, Nothing, Nothing,
Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, No
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#WeaveSandBox#225".slider_crank_mm!), Matrix{Float64}, Nothing, Nothing, No
thing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothi
ng, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing,
Nothing}, Vector{Float64}, SciMLBase.NullParameters}, SciMLBase.UJacobianW
rapper{true, SciMLBase.ODEFunction{true, SciMLBase.FullSpecialize, typeof(M
ain.var"##WeaveSandBox#225".slider_crank_mm!), Matrix{Float64}, Nothing, No
thing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothi
ng, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing,
Nothing, Nothing}, Float64, SciMLBase.NullParameters}, LinearSolve.LinearC
ache{Matrix{Float64}, Vector{Float64}, Vector{Float64}, SciMLBase.NullParam
eters, LinearSolve.DefaultLinearSolver, LinearSolve.DefaultLinearSolverInit
{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, LinearAlgebra.Q
RCompactWY{Float64, Matrix{Float64}, Matrix{Float64}}, Nothing, Nothing, No
thing, Nothing, Nothing, Nothing, Tuple{LinearAlgebra.LU{Float64, Matrix{Fl
oat64}, Vector{Int64}}, Vector{Int64}}, Tuple{LinearAlgebra.LU{Float64, Mat
rix{Float64}, Vector{Int64}}, Vector{Int64}}, Nothing, Nothing, Nothing, Li
nearAlgebra.SVD{Float64, Float64, Matrix{Float64}, Vector{Float64}}, Linear
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Matrix{Float64}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{
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econditioner{LinearAlgebra.Diagonal{Float64, Vector{Float64}}}, LinearAlgeb
ra.Diagonal{Float64, Vector{Float64}}, Float64, LinearSolve.LinearVerbosity
{SciMLLogging.Silent, SciMLLogging.Silent, SciMLLogging.Silent, SciMLLoggin
g.Silent, SciMLLogging.Silent, SciMLLogging.Silent, SciMLLogging.Silent, Sc
iMLLogging.Silent, SciMLLogging.WarnLevel, SciMLLogging.WarnLevel, SciMLLog
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t.ForwardDiffTwoArgDerivativePrep{Tuple{SciMLBase.TimeGradientWrapper{true,
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ff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Vector{ForwardDiff.Dual{Forw
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, DifferentiationInterfaceForwardDiffExt.ForwardDiffTwoArgDerivativePrep{Tu
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mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.v
ar"#_RGF_ModTag", (0x4661a20f, 0xc7cca64b, 0x7a70f6cf, 0x6d73e89a, 0xb01332
43), Nothing}}}))), [1.0 0.0 … 0.0 0.0; 0.0 1.0 … 0.0 0.0; … ; 0.0 0.0 … 0.
0 0.0; 0.0 0.0 … 0.0 0.0], nothing, nothing, nothing, nothing, nothing, not
hing, nothing, nothing, nothing, nothing, nothing, nothing, ModelingToolkit
.ObservedFunctionCache{ModelingToolkit.ODESystem}(Model sys:
Equations (13):
13 standard: see equations(sys)
Unknowns (13): see unknowns(sys)
vq₄(t) [defaults to -2.68939e-6]
q₄(t) [defaults to 1.69328e-5]
vq₂(t) [defaults to 0.00463434]
vq₁(t) [defaults to 0.444896]
⋮
Observed (14): see observed(sys), Dict{Any, Any}(), false, false, ModelingT
oolkit, false, true), nothing, Model sys:
Equations (13):
13 standard: see equations(sys)
Unknowns (13): see unknowns(sys)
vq₄(t) [defaults to -2.68939e-6]
q₄(t) [defaults to 1.69328e-5]
vq₂(t) [defaults to 0.00463434]
vq₁(t) [defaults to 0.444896]
⋮
Observed (14): see observed(sys), SciMLBase.OverrideInitData{SciMLBase.Nonl
inearLeastSquaresProblem{Vector{Float64}, true, ModelingToolkit.MTKParamete
rs{Vector{Float64}, StaticArraysCore.SizedVector{0, Float64, Vector{Float64
}}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, SciMLBase.NonlinearFunction{true,
SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionWrapper{(2, 2, t
rue), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :__
_mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"
#_RGF_ModTag", (0x855d74ab, 0xd2df28ae, 0xeb3ecdd0, 0x325306af, 0xd16f567f)
, Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__
mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Modeli
ngToolkit.var"#_RGF_ModTag", (0xc8a21f76, 0xd50266a8, 0x36ae5075, 0x4ece6d0
a, 0x4e546efd), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Not
hing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothin
g, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.NonlinearSystem},
Nothing, ModelingToolkit.NonlinearSystem, Vector{Float64}, Nothing}, Base.P
airs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, Nothing, Nothing}, typeof(Mo
delingToolkit.update_initializeprob!), ComposedFunction{ComposedFunction{ty
peof(identity), typeof(ModelingToolkit.safe_float)}, SymbolicIndexingInterf
ace.TimeIndependentObservedFunction{ModelingToolkit.GeneratedFunctionWrappe
r{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_
arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingTo
olkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x5560ce01, 0x991a4cdf, 0
x392020a7), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:
ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTa
g", ModelingToolkit.var"#_RGF_ModTag", (0x2b19e578, 0x47f62e68, 0x3f23a85d,
0xb87b692a, 0xb5777171), Nothing}}}}, ModelingToolkit.var"#initprobpmap_sp
lit#810"{ModelingToolkit.var"#_getter#806"{Tuple{Returns{StaticArraysCore.S
izedVector{0, Float64, Vector{Float64}}}, ComposedFunction{ModelingToolkit.
PConstructorApplicator{typeof(identity)}, ModelingToolkit.ObservedWrapper{f
alse, ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGenerat
edFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___),
ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x38
3e1f76, 0x30e3ca66, 0xe27ee296, 0x7de466bf, 0xddedf6e9), Nothing}, RuntimeG
eneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkpa
rameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_
ModTag", (0xdef1fe73, 0x41a6768b, 0x43614868, 0x9db8eb5f, 0xb69f9719), Noth
ing}}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}}, ModelingT
oolkit.InitializationMetadata{ModelingToolkit.ReconstructInitializeprob{Mod
elingToolkit.var"#_getter#806"{Tuple{ComposedFunction{ModelingToolkit.PCons
tructorApplicator{typeof(identity)}, ModelingToolkit.ObservedWrapper{true,
ModelingToolkit.GeneratedFunctionWrapper{(2, 3, true), RuntimeGeneratedFunc
tions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), Mo
delingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x7e79
da91, 0xd20b440a, 0x8f31de5e, 0xb3bf1671, 0x1e4c890d), Nothing}, RuntimeGen
eratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkpara
meters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RG
F_ModTag", (0xdc0e8bfb, 0xe657b82a, 0x2b04a79c, 0xdd2049fc, 0x2f912348), No
thing}}}}, Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}
}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}, ComposedFunctio
n{typeof(identity), SymbolicIndexingInterface.TimeDependentObservedFunction
{SymbolicIndexingInterface.ContinuousTimeseries, ModelingToolkit.GeneratedF
unctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunc
tion{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_Mo
dTag", ModelingToolkit.var"#_RGF_ModTag", (0xe2dbe4c4, 0x8637425f, 0xf9877c
30, 0xc6a732b9, 0xb3aed46a), Nothing}, RuntimeGeneratedFunctions.RuntimeGen
eratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingTo
olkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc0ff0587, 0x
8943b463, 0x759a7721, 0x55ab8be5, 0xe5da0c74), Nothing}}, true}}}, Modeling
Toolkit.GetUpdatedU0{SymbolicIndexingInterface.TimeIndependentObservedFunct
ion{ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGenerated
Functions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), Mo
delingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x402c
48b5, 0xfa2314b8, 0x4a877dea, 0xd8553b68, 0xe8202d4a), Nothing}, RuntimeGen
eratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkpara
meters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_Mo
dTag", (0xefb5629c, 0x6f14cbd6, 0xfff3a505, 0x6fdc0cc0, 0x6dc034e6), Nothin
g}}}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingIn
terface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameter
Index{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}}, No
thing}}, ModelingToolkit.SetInitialUnknowns{SymbolicIndexingInterface.Multi
pleSetters{Vector{SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIn
dexingInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStruc
tures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}}}}}, Val{true}}
(SciMLBase.NonlinearLeastSquaresProblem{Vector{Float64}, true, ModelingTool
kit.MTKParameters{Vector{Float64}, StaticArraysCore.SizedVector{0, Float64,
Vector{Float64}}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, SciMLBase.Nonlinear
Function{true, SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionW
rapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:_
_mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Model
ingToolkit.var"#_RGF_ModTag", (0x855d74ab, 0xd2df28ae, 0xeb3ecdd0, 0x325306
af, 0xd16f567f), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFuncti
on{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_
ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc8a21f76, 0xd50266a8, 0x36ae
5075, 0x4ece6d0a, 0x4e546efd), Nothing}}, LinearAlgebra.UniformScaling{Bool
}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing,
Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.Non
linearSystem}, Nothing, ModelingToolkit.NonlinearSystem, Vector{Float64}, N
othing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, Nothing, Noth
ing}(SciMLBase.NonlinearFunction{true, SciMLBase.FullSpecialize, ModelingTo
olkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.Runt
imeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.
var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x855d74ab, 0xd2df28
ae, 0xeb3ecdd0, 0x325306af, 0xd16f567f), Nothing}, RuntimeGeneratedFunction
s.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), Mo
delingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc8a2
1f76, 0xd50266a8, 0x36ae5075, 0x4ece6d0a, 0x4e546efd), Nothing}}, LinearAlg
ebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Not
hing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionC
ache{ModelingToolkit.NonlinearSystem}, Nothing, ModelingToolkit.NonlinearSy
stem, Vector{Float64}, Nothing}(ModelingToolkit.GeneratedFunctionWrapper{(2
, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_
1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolki
t.var"#_RGF_ModTag", (0x855d74ab, 0xd2df28ae, 0xeb3ecdd0, 0x325306af, 0xd16
f567f), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋ou
t, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag",
ModelingToolkit.var"#_RGF_ModTag", (0xc8a21f76, 0xd50266a8, 0x36ae5075, 0x4
ece6d0a, 0x4e546efd), Nothing}}(RuntimeGeneratedFunctions.RuntimeGeneratedF
unction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_Mod
Tag", ModelingToolkit.var"#_RGF_ModTag", (0x855d74ab, 0xd2df28ae, 0xeb3ecdd
0, 0x325306af, 0xd16f567f), Nothing}(nothing), RuntimeGeneratedFunctions.Ru
ntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), Modeli
ngToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc8a21f76
, 0xd50266a8, 0x36ae5075, 0x4ece6d0a, 0x4e546efd), Nothing}(nothing)), Line
arAlgebra.UniformScaling{Bool}(true), nothing, nothing, nothing, nothing, n
othing, nothing, nothing, nothing, nothing, nothing, ModelingToolkit.Observ
edFunctionCache{ModelingToolkit.NonlinearSystem}(Model sys:
Equations (10):
10 standard: see equations(sys)
Unknowns (1): see unknowns(sys)
vφ2ˍt(t) [defaults to -74.9958]
Parameters (45): see parameters(sys)
t
Initial(vφ1ˍt(t)) [defaults to false]
Initial(vφ1ˍtt(t)) [defaults to false]
Initial(vq₄ˍt(t)) [defaults to false]
⋮
Observed (26): see observed(sys), Dict{Any, Any}(SymbolicUtils.BasicSymboli
c{Real}[vq₄(t), q₄(t), vq₂(t), vq₁(t), vq₃(t), q₁(t), q₂(t), q₃(t), φ2ˍt(t)
, vq₄ˍt(t), φ2(t), λ₁(t), φ2ˍtt(t)] => ModelingToolkit.GeneratedFunctionWra
pper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__m
tk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Modelin
gToolkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x5560ce01, 0x991a4cdf
, 0x392020a7), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction
{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_Mo
dTag", ModelingToolkit.var"#_RGF_ModTag", (0x2b19e578, 0x47f62e68, 0x3f23a8
5d, 0xb87b692a, 0xb5777171), Nothing}}(RuntimeGeneratedFunctions.RuntimeGen
eratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_
RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x
5560ce01, 0x991a4cdf, 0x392020a7), Nothing}(nothing), RuntimeGeneratedFunct
ions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___),
ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x2
b19e578, 0x47f62e68, 0x3f23a85d, 0xb87b692a, 0xb5777171), Nothing}(nothing)
), Any[vq₄ˍt(t), φ2ˍtt(t), φ2ˍt(t)] => ModelingToolkit.GeneratedFunctionWra
pper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__m
tk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Modelin
gToolkit.var"#_RGF_ModTag", (0x59806009, 0x122eca51, 0xd6164a75, 0x9414c9c0
, 0xe211bcbc), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction
{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_Mo
dTag", ModelingToolkit.var"#_RGF_ModTag", (0x44b04ca3, 0xf8eac98b, 0x8198dd
8b, 0xa7a5108c, 0x9f72ce11), Nothing}}(RuntimeGeneratedFunctions.RuntimeGen
eratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_
RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x59806009, 0x122eca51, 0x
d6164a75, 0x9414c9c0, 0xe211bcbc), Nothing}(nothing), RuntimeGeneratedFunct
ions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___),
ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x4
4b04ca3, 0xf8eac98b, 0x8198dd8b, 0xa7a5108c, 0x9f72ce11), Nothing}(nothing)
)), false, false, ModelingToolkit, false, true), nothing, Model sys:
Equations (10):
10 standard: see equations(sys)
Unknowns (1): see unknowns(sys)
vφ2ˍt(t) [defaults to -74.9958]
Parameters (45): see parameters(sys)
t
Initial(vφ1ˍt(t)) [defaults to false]
Initial(vφ1ˍtt(t)) [defaults to false]
Initial(vq₄ˍt(t)) [defaults to false]
⋮
Observed (26): see observed(sys), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0], nothing), [0.0], ModelingToolkit.MTKParameters{Vector{Float64},
StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}, Tuple{}, Tuple{}
, Tuple{}, Tuple{}}([0.0, 0.0, 0.0, 0.0, -2.68938672e-6, 382.45895095266985
, 0.0, 1.69327969e-5, 150.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.033398
63e-5, 0.0, 0.0, 0.0], Float64[], (), (), (), ()), nothing, nothing, Base.P
airs{Symbol, Union{}, Tuple{}, @NamedTuple{}}()), ModelingToolkit.update_in
itializeprob!, identity ∘ ModelingToolkit.safe_float ∘ SymbolicIndexingInte
rface.TimeIndependentObservedFunction{ModelingToolkit.GeneratedFunctionWrap
per{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mt
k_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Modeling
Toolkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x5560ce01, 0x991a4cdf,
0x392020a7), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{
(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_Mod
Tag", ModelingToolkit.var"#_RGF_ModTag", (0x2b19e578, 0x47f62e68, 0x3f23a85
d, 0xb87b692a, 0xb5777171), Nothing}}}(ModelingToolkit.GeneratedFunctionWra
pper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__m
tk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Modelin
gToolkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x5560ce01, 0x991a4cdf
, 0x392020a7), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction
{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_Mo
dTag", ModelingToolkit.var"#_RGF_ModTag", (0x2b19e578, 0x47f62e68, 0x3f23a8
5d, 0xb87b692a, 0xb5777171), Nothing}}(RuntimeGeneratedFunctions.RuntimeGen
eratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_
RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x
5560ce01, 0x991a4cdf, 0x392020a7), Nothing}(nothing), RuntimeGeneratedFunct
ions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___),
ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x2
b19e578, 0x47f62e68, 0x3f23a85d, 0xb87b692a, 0xb5777171), Nothing}(nothing)
)), ModelingToolkit.var"#initprobpmap_split#810"{ModelingToolkit.var"#_gett
er#806"{Tuple{Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float
64}}}, ComposedFunction{ModelingToolkit.PConstructorApplicator{typeof(ident
ity)}, ModelingToolkit.ObservedWrapper{false, ModelingToolkit.GeneratedFunc
tionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunctio
n{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag",
ModelingToolkit.var"#_RGF_ModTag", (0x383e1f76, 0x30e3ca66, 0xe27ee296, 0x7
de466bf, 0xddedf6e9), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedF
unction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#
_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xdef1fe73, 0x41a6768b, 0
x43614868, 0x9db8eb5f, 0xb69f9719), Nothing}}}}, Returns{Tuple{}}, Returns{
Tuple{}}, Returns{Tuple{}}}}}(ModelingToolkit.var"#_getter#806"{Tuple{Retur
ns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}}, ComposedFunc
tion{ModelingToolkit.PConstructorApplicator{typeof(identity)}, ModelingTool
kit.ObservedWrapper{false, ModelingToolkit.GeneratedFunctionWrapper{(2, 2,
true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :_
__mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var
"#_RGF_ModTag", (0x383e1f76, 0x30e3ca66, 0xe27ee296, 0x7de466bf, 0xddedf6e9
), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :_
_mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Model
ingToolkit.var"#_RGF_ModTag", (0xdef1fe73, 0x41a6768b, 0x43614868, 0x9db8eb
5f, 0xb69f9719), Nothing}}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{T
uple{}}}}((Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}
}}(Float64[]), ModelingToolkit.PConstructorApplicator{typeof(identity)}(ide
ntity) ∘ ModelingToolkit.ObservedWrapper{false, ModelingToolkit.GeneratedFu
nctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunct
ion{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag"
, ModelingToolkit.var"#_RGF_ModTag", (0x383e1f76, 0x30e3ca66, 0xe27ee296, 0
x7de466bf, 0xddedf6e9), Nothing}, RuntimeGeneratedFunctions.RuntimeGenerate
dFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var
"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xdef1fe73, 0x41a6768b,
0x43614868, 0x9db8eb5f, 0xb69f9719), Nothing}}}(ModelingToolkit.GeneratedF
unctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunc
tion{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag
", ModelingToolkit.var"#_RGF_ModTag", (0x383e1f76, 0x30e3ca66, 0xe27ee296,
0x7de466bf, 0xddedf6e9), Nothing}, RuntimeGeneratedFunctions.RuntimeGenerat
edFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.va
r"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xdef1fe73, 0x41a6768b
, 0x43614868, 0x9db8eb5f, 0xb69f9719), Nothing}}(RuntimeGeneratedFunctions.
RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingTool
kit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x383e1f76, 0x30
e3ca66, 0xe27ee296, 0x7de466bf, 0xddedf6e9), Nothing}(nothing), RuntimeGene
ratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparam
eters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_Mod
Tag", (0xdef1fe73, 0x41a6768b, 0x43614868, 0x9db8eb5f, 0xb69f9719), Nothing
}(nothing))), Returns{Tuple{}}(()), Returns{Tuple{}}(()), Returns{Tuple{}}(
())))), ModelingToolkit.InitializationMetadata{ModelingToolkit.ReconstructI
nitializeprob{ModelingToolkit.var"#_getter#806"{Tuple{ComposedFunction{Mode
lingToolkit.PConstructorApplicator{typeof(identity)}, ModelingToolkit.Obser
vedWrapper{true, ModelingToolkit.GeneratedFunctionWrapper{(2, 3, true), Run
timeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparam
eters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF
_ModTag", (0x7e79da91, 0xd20b440a, 0x8f31de5e, 0xb3bf1671, 0x1e4c890d), Not
hing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_a
rg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", Modelin
gToolkit.var"#_RGF_ModTag", (0xdc0e8bfb, 0xe657b82a, 0x2b04a79c, 0xdd2049fc
, 0x2f912348), Nothing}}}}, Returns{StaticArraysCore.SizedVector{0, Float64
, Vector{Float64}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}
, ComposedFunction{typeof(identity), SymbolicIndexingInterface.TimeDependen
tObservedFunction{SymbolicIndexingInterface.ContinuousTimeseries, ModelingT
oolkit.GeneratedFunctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.Run
timeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToo
lkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe2dbe4c4, 0x8
637425f, 0xf9877c30, 0xc6a732b9, 0xb3aed46a), Nothing}, RuntimeGeneratedFun
ctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___
, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag"
, (0xc0ff0587, 0x8943b463, 0x759a7721, 0x55ab8be5, 0xe5da0c74), Nothing}},
true}}}, ModelingToolkit.GetUpdatedU0{SymbolicIndexingInterface.TimeIndepen
dentObservedFunction{ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true),
RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkp
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hing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_a
rg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToo
lkit.var"#_RGF_ModTag", (0xefb5629c, 0x6f14cbd6, 0xfff3a505, 0x6fdc0cc0, 0x
6dc034e6), Nothing}}}, SymbolicIndexingInterface.MultipleParametersGetter{S
ymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInter
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als, Int64}}}, Nothing}}, ModelingToolkit.SetInitialUnknowns{SymbolicIndexi
ngInterface.MultipleSetters{Vector{SymbolicIndexingInterface.ParameterHookW
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, x₃(t) => Initial(x₃(t)), q₁(t) => Initial(q₁(t)), λ₁(t) => Initial(λ₁(t))
, q₃(t) => Initial(q₃(t)), vq₄(t) => Initial(vq₄(t))…), Dict{Any, Any}(Init
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85, Initial(λ₂ˍt(t)) => false, Initial(q₄(t)) => 1.69327969e-5, Initial(vφ1
(t)) => 150.0, Initial(vx₃ˍt(t)) => false, Initial(x₃ˍtt(t)) => false…), Di
ct{Any, Any}(), Symbolics.Equation[], true, ModelingToolkit.ReconstructInit
ializeprob{ModelingToolkit.var"#_getter#806"{Tuple{ComposedFunction{Modelin
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servedFunction{SymbolicIndexingInterface.ContinuousTimeseries, ModelingTool
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:t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag",
(0x7e79da91, 0xd20b440a, 0x8f31de5e, 0xb3bf1671, 0x1e4c890d), Nothing}, Ru
ntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :__
_mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.
var"#_RGF_ModTag", (0xdc0e8bfb, 0xe657b82a, 0x2b04a79c, 0xdd2049fc, 0x2f912
348), Nothing}}}}, Returns{StaticArraysCore.SizedVector{0, Float64, Vector{
Float64}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}((Modelin
gToolkit.PConstructorApplicator{typeof(identity)}(identity) ∘ ModelingToolk
it.ObservedWrapper{true, ModelingToolkit.GeneratedFunctionWrapper{(2, 3, tr
ue), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___
mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.v
ar"#_RGF_ModTag", (0x7e79da91, 0xd20b440a, 0x8f31de5e, 0xb3bf1671, 0x1e4c89
0d), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out,
:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag",
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dd2049fc, 0x2f912348), Nothing}}}(ModelingToolkit.GeneratedFunctionWrapper{
(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_ar
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Toolkit.var"#_RGF_ModTag", (0x7e79da91, 0xd20b440a, 0x8f31de5e, 0xb3bf1671,
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(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF
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4a79c, 0xdd2049fc, 0x2f912348), Nothing}}(RuntimeGeneratedFunctions.Runtime
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40a, 0x8f31de5e, 0xb3bf1671, 0x1e4c890d), Nothing}(nothing), RuntimeGenerat
edFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparamete
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g}(nothing))), Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Floa
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e{}}(()))), identity ∘ SymbolicIndexingInterface.TimeDependentObservedFunct
ion{SymbolicIndexingInterface.ContinuousTimeseries, ModelingToolkit.Generat
edFunctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedF
unction{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF
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77c30, 0xc6a732b9, 0xb3aed46a), Nothing}, RuntimeGeneratedFunctions.Runtime
GeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), Modelin
gToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc0ff0587,
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IndexingInterface.ContinuousTimeseries(), ModelingToolkit.GeneratedFunction
Wrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:
__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag",
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6a732b9, 0xb3aed46a), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedF
unction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.v
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.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), Modelin
gToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe2dbe4c4,
0x8637425f, 0xf9877c30, 0xc6a732b9, 0xb3aed46a), Nothing}(nothing), Runtim
eGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtk
parameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"
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xe8202d4a), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:
ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTa
g", ModelingToolkit.var"#_RGF_ModTag", (0xefb5629c, 0x6f14cbd6, 0xfff3a505,
0x6fdc0cc0, 0x6dc034e6), Nothing}}}, SymbolicIndexingInterface.MultiplePar
ametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{Symbol
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gToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.R
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ions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___),
ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe
fb5629c, 0x6f14cbd6, 0xfff3a505, 0x6fdc0cc0, 0x6dc034e6), Nothing}}}(Modeli
ngToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.
RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingTool
kit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x402c48b5, 0xfa
2314b8, 0x4a877dea, 0xd8553b68, 0xe8202d4a), Nothing}, RuntimeGeneratedFunc
tions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___)
, ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x
efb5629c, 0x6f14cbd6, 0xfff3a505, 0x6fdc0cc0, 0x6dc034e6), Nothing}}(Runtim
eGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparamete
rs___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag
", (0x402c48b5, 0xfa2314b8, 0x4a877dea, 0xd8553b68, 0xe8202d4a), Nothing}(n
othing), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk
_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingT
oolkit.var"#_RGF_ModTag", (0xefb5629c, 0x6f14cbd6, 0xfff3a505, 0x6fdc0cc0,
0x6dc034e6), Nothing}(nothing))), SymbolicIndexingInterface.MultipleParamet
ersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIn
dexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStruc
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nitials, Int64}}(ModelingToolkit.ParameterIndex{SciMLStructures.Initials, I
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ParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int
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tructures.Initials(), 20, false)), SymbolicIndexingInterface.GetParameterIn
dex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}(Modeli
ngToolkit.ParameterIndex{SciMLStructures.Initials, Int64}(SciMLStructures.I
nitials(), 24, false)), SymbolicIndexingInterface.GetParameterIndex{Modelin
gToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}(ModelingToolkit.P
arameterIndex{SciMLStructures.Initials, Int64}(SciMLStructures.Initials(),
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rameterIndex{SciMLStructures.Initials, Int64}}(ModelingToolkit.ParameterInd
ex{SciMLStructures.Initials, Int64}(SciMLStructures.Initials(), 34, false))
, SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterInde
x{SciMLStructures.Initials, Int64}}(ModelingToolkit.ParameterIndex{SciMLStr
uctures.Initials, Int64}(SciMLStructures.Initials(), 32, false)), SymbolicI
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tials, Int64}(SciMLStructures.Initials(), 41, false)), SymbolicIndexingInte
rface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Init
ials, Int64}}(ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int6
4}(SciMLStructures.Initials(), 30, false)), SymbolicIndexingInterface.GetPa
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}}(ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}(SciMLStr
uctures.Initials(), 3, false)), SymbolicIndexingInterface.GetParameterIndex
{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}(ModelingT
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false)), SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.Param
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nothing)), ModelingToolkit.SetInitialUnknowns{SymbolicIndexingInterface.Mul
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se)), Initial(vq₄(t))), SymbolicIndexingInterface.ParameterHookWrapper{Symb
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ngInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructure
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cIndexingInterface.ParameterHookWrapper{SymbolicIndexingInterface.SetParame
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tial(q₂(t))), SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexi
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vq₄ˍt(t))), SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexing
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als, Int64}}(ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64
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gInterface.ParameterHookWrapper{SymbolicIndexingInterface.SetParameterIndex
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lingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}(ModelingToolki
t.ParameterIndex{SciMLStructures.Initials, Int64}(SciMLStructures.Initials(
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ndex{SciMLStructures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}(
SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{
SciMLStructures.Initials, Int64}}(ModelingToolkit.ParameterIndex{SciMLStruc
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tt(t)))]))), Val{true}()), nothing), [-2.68938672e-6, 1.69327969e-5, 0.0046
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ModelingToolkit.MTKParameters{StaticArraysCore.SizedVector{0, Float64, Vect
or{Float64}}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}(Float64[
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, 1.69327969e-5, 150.0, -5062.19492472297, -5062.194924724621 … 0.0, 150.
0, 0.0, 0.0, 0.0, 0.0, 1.03339863e-5, 0.0, -0.0013444290087241812, 0.0], ()
, (), (), ()), Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}(), SciML
Base.StandardODEProblem()), OrdinaryDiffEqRosenbrock.Rodas5P{1, ADTypes.Aut
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}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1
, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToo
lkit.var"#_RGF_ModTag", (0x4661a20f, 0xc7cca64b, 0x7a70f6cf, 0x6d73e89a, 0x
b0133243), Nothing}}}))), [1.0 0.0 … 0.0 0.0; 0.0 1.0 … 0.0 0.0; … ; 0.0 0.
0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0], nothing, nothing, nothing, nothing, nothin
g, nothing, nothing, nothing, nothing, nothing, nothing, nothing, ModelingT
oolkit.ObservedFunctionCache{ModelingToolkit.ODESystem}(Model sys:
Equations (13):
13 standard: see equations(sys)
Unknowns (13): see unknowns(sys)
vq₄(t) [defaults to -2.68939e-6]
q₄(t) [defaults to 1.69328e-5]
vq₂(t) [defaults to 0.00463434]
vq₁(t) [defaults to 0.444896]
⋮
Observed (14): see observed(sys), Dict{Any, Any}(), false, false, ModelingT
oolkit, false, true), nothing, Model sys:
Equations (13):
13 standard: see equations(sys)
Unknowns (13): see unknowns(sys)
vq₄(t) [defaults to -2.68939e-6]
q₄(t) [defaults to 1.69328e-5]
vq₂(t) [defaults to 0.00463434]
vq₁(t) [defaults to 0.444896]
⋮
Observed (14): see observed(sys), SciMLBase.OverrideInitData{SciMLBase.Nonl
inearLeastSquaresProblem{Vector{Float64}, true, ModelingToolkit.MTKParamete
rs{Vector{Float64}, StaticArraysCore.SizedVector{0, Float64, Vector{Float64
}}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, SciMLBase.NonlinearFunction{true,
SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionWrapper{(2, 2, t
rue), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :__
_mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"
#_RGF_ModTag", (0x855d74ab, 0xd2df28ae, 0xeb3ecdd0, 0x325306af, 0xd16f567f)
, Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__
mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Modeli
ngToolkit.var"#_RGF_ModTag", (0xc8a21f76, 0xd50266a8, 0x36ae5075, 0x4ece6d0
a, 0x4e546efd), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Not
hing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothin
g, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.NonlinearSystem},
Nothing, ModelingToolkit.NonlinearSystem, Vector{Float64}, Nothing}, Base.P
airs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, Nothing, Nothing}, typeof(Mo
delingToolkit.update_initializeprob!), ComposedFunction{ComposedFunction{ty
peof(identity), typeof(ModelingToolkit.safe_float)}, SymbolicIndexingInterf
ace.TimeIndependentObservedFunction{ModelingToolkit.GeneratedFunctionWrappe
r{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_
arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingTo
olkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x5560ce01, 0x991a4cdf, 0
x392020a7), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:
ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTa
g", ModelingToolkit.var"#_RGF_ModTag", (0x2b19e578, 0x47f62e68, 0x3f23a85d,
0xb87b692a, 0xb5777171), Nothing}}}}, ModelingToolkit.var"#initprobpmap_sp
lit#810"{ModelingToolkit.var"#_getter#806"{Tuple{Returns{StaticArraysCore.S
izedVector{0, Float64, Vector{Float64}}}, ComposedFunction{ModelingToolkit.
PConstructorApplicator{typeof(identity)}, ModelingToolkit.ObservedWrapper{f
alse, ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGenerat
edFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___),
ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x38
3e1f76, 0x30e3ca66, 0xe27ee296, 0x7de466bf, 0xddedf6e9), Nothing}, RuntimeG
eneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkpa
rameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_
ModTag", (0xdef1fe73, 0x41a6768b, 0x43614868, 0x9db8eb5f, 0xb69f9719), Noth
ing}}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}}, ModelingT
oolkit.InitializationMetadata{ModelingToolkit.ReconstructInitializeprob{Mod
elingToolkit.var"#_getter#806"{Tuple{ComposedFunction{ModelingToolkit.PCons
tructorApplicator{typeof(identity)}, ModelingToolkit.ObservedWrapper{true,
ModelingToolkit.GeneratedFunctionWrapper{(2, 3, true), RuntimeGeneratedFunc
tions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), Mo
delingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x7e79
da91, 0xd20b440a, 0x8f31de5e, 0xb3bf1671, 0x1e4c890d), Nothing}, RuntimeGen
eratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkpara
meters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RG
F_ModTag", (0xdc0e8bfb, 0xe657b82a, 0x2b04a79c, 0xdd2049fc, 0x2f912348), No
thing}}}}, Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}
}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}, ComposedFunctio
n{typeof(identity), SymbolicIndexingInterface.TimeDependentObservedFunction
{SymbolicIndexingInterface.ContinuousTimeseries, ModelingToolkit.GeneratedF
unctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunc
tion{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_Mo
dTag", ModelingToolkit.var"#_RGF_ModTag", (0xe2dbe4c4, 0x8637425f, 0xf9877c
30, 0xc6a732b9, 0xb3aed46a), Nothing}, RuntimeGeneratedFunctions.RuntimeGen
eratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingTo
olkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc0ff0587, 0x
8943b463, 0x759a7721, 0x55ab8be5, 0xe5da0c74), Nothing}}, true}}}, Modeling
Toolkit.GetUpdatedU0{SymbolicIndexingInterface.TimeIndependentObservedFunct
ion{ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGenerated
Functions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), Mo
delingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x402c
48b5, 0xfa2314b8, 0x4a877dea, 0xd8553b68, 0xe8202d4a), Nothing}, RuntimeGen
eratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkpara
meters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_Mo
dTag", (0xefb5629c, 0x6f14cbd6, 0xfff3a505, 0x6fdc0cc0, 0x6dc034e6), Nothin
g}}}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingIn
terface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameter
Index{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}}, No
thing}}, ModelingToolkit.SetInitialUnknowns{SymbolicIndexingInterface.Multi
pleSetters{Vector{SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIn
dexingInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStruc
tures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}}}}}, Val{true}}
(SciMLBase.NonlinearLeastSquaresProblem{Vector{Float64}, true, ModelingTool
kit.MTKParameters{Vector{Float64}, StaticArraysCore.SizedVector{0, Float64,
Vector{Float64}}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, SciMLBase.Nonlinear
Function{true, SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionW
rapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:_
_mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Model
ingToolkit.var"#_RGF_ModTag", (0x855d74ab, 0xd2df28ae, 0xeb3ecdd0, 0x325306
af, 0xd16f567f), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFuncti
on{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_
ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc8a21f76, 0xd50266a8, 0x36ae
5075, 0x4ece6d0a, 0x4e546efd), Nothing}}, LinearAlgebra.UniformScaling{Bool
}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing,
Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.Non
linearSystem}, Nothing, ModelingToolkit.NonlinearSystem, Vector{Float64}, N
othing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, Nothing, Noth
ing}(SciMLBase.NonlinearFunction{true, SciMLBase.FullSpecialize, ModelingTo
olkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.Runt
imeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.
var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x855d74ab, 0xd2df28
ae, 0xeb3ecdd0, 0x325306af, 0xd16f567f), Nothing}, RuntimeGeneratedFunction
s.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), Mo
delingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc8a2
1f76, 0xd50266a8, 0x36ae5075, 0x4ece6d0a, 0x4e546efd), Nothing}}, LinearAlg
ebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Not
hing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionC
ache{ModelingToolkit.NonlinearSystem}, Nothing, ModelingToolkit.NonlinearSy
stem, Vector{Float64}, Nothing}(ModelingToolkit.GeneratedFunctionWrapper{(2
, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_
1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolki
t.var"#_RGF_ModTag", (0x855d74ab, 0xd2df28ae, 0xeb3ecdd0, 0x325306af, 0xd16
f567f), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋ou
t, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag",
ModelingToolkit.var"#_RGF_ModTag", (0xc8a21f76, 0xd50266a8, 0x36ae5075, 0x4
ece6d0a, 0x4e546efd), Nothing}}(RuntimeGeneratedFunctions.RuntimeGeneratedF
unction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_Mod
Tag", ModelingToolkit.var"#_RGF_ModTag", (0x855d74ab, 0xd2df28ae, 0xeb3ecdd
0, 0x325306af, 0xd16f567f), Nothing}(nothing), RuntimeGeneratedFunctions.Ru
ntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), Modeli
ngToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc8a21f76
, 0xd50266a8, 0x36ae5075, 0x4ece6d0a, 0x4e546efd), Nothing}(nothing)), Line
arAlgebra.UniformScaling{Bool}(true), nothing, nothing, nothing, nothing, n
othing, nothing, nothing, nothing, nothing, nothing, ModelingToolkit.Observ
edFunctionCache{ModelingToolkit.NonlinearSystem}(Model sys:
Equations (10):
10 standard: see equations(sys)
Unknowns (1): see unknowns(sys)
vφ2ˍt(t) [defaults to -74.9958]
Parameters (45): see parameters(sys)
t
Initial(vφ1ˍt(t)) [defaults to false]
Initial(vφ1ˍtt(t)) [defaults to false]
Initial(vq₄ˍt(t)) [defaults to false]
⋮
Observed (26): see observed(sys), Dict{Any, Any}(SymbolicUtils.BasicSymboli
c{Real}[vq₄(t), q₄(t), vq₂(t), vq₁(t), vq₃(t), q₁(t), q₂(t), q₃(t), φ2ˍt(t)
, vq₄ˍt(t), φ2(t), λ₁(t), φ2ˍtt(t)] => ModelingToolkit.GeneratedFunctionWra
pper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__m
tk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Modelin
gToolkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x5560ce01, 0x991a4cdf
, 0x392020a7), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction
{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_Mo
dTag", ModelingToolkit.var"#_RGF_ModTag", (0x2b19e578, 0x47f62e68, 0x3f23a8
5d, 0xb87b692a, 0xb5777171), Nothing}}(RuntimeGeneratedFunctions.RuntimeGen
eratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_
RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x
5560ce01, 0x991a4cdf, 0x392020a7), Nothing}(nothing), RuntimeGeneratedFunct
ions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___),
ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x2
b19e578, 0x47f62e68, 0x3f23a85d, 0xb87b692a, 0xb5777171), Nothing}(nothing)
), Any[vq₄ˍt(t), φ2ˍtt(t), φ2ˍt(t)] => ModelingToolkit.GeneratedFunctionWra
pper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__m
tk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Modelin
gToolkit.var"#_RGF_ModTag", (0x59806009, 0x122eca51, 0xd6164a75, 0x9414c9c0
, 0xe211bcbc), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction
{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_Mo
dTag", ModelingToolkit.var"#_RGF_ModTag", (0x44b04ca3, 0xf8eac98b, 0x8198dd
8b, 0xa7a5108c, 0x9f72ce11), Nothing}}(RuntimeGeneratedFunctions.RuntimeGen
eratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_
RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x59806009, 0x122eca51, 0x
d6164a75, 0x9414c9c0, 0xe211bcbc), Nothing}(nothing), RuntimeGeneratedFunct
ions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___),
ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x4
4b04ca3, 0xf8eac98b, 0x8198dd8b, 0xa7a5108c, 0x9f72ce11), Nothing}(nothing)
)), false, false, ModelingToolkit, false, true), nothing, Model sys:
Equations (10):
10 standard: see equations(sys)
Unknowns (1): see unknowns(sys)
vφ2ˍt(t) [defaults to -74.9958]
Parameters (45): see parameters(sys)
t
Initial(vφ1ˍt(t)) [defaults to false]
Initial(vφ1ˍtt(t)) [defaults to false]
Initial(vq₄ˍt(t)) [defaults to false]
⋮
Observed (26): see observed(sys), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0], nothing), [0.0], ModelingToolkit.MTKParameters{Vector{Float64},
StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}, Tuple{}, Tuple{}
, Tuple{}, Tuple{}}([0.0, 0.0, 0.0, 0.0, -2.68938672e-6, 382.45895095266985
, 0.0, 1.69327969e-5, 150.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.033398
63e-5, 0.0, 0.0, 0.0], Float64[], (), (), (), ()), nothing, nothing, Base.P
airs{Symbol, Union{}, Tuple{}, @NamedTuple{}}()), ModelingToolkit.update_in
itializeprob!, identity ∘ ModelingToolkit.safe_float ∘ SymbolicIndexingInte
rface.TimeIndependentObservedFunction{ModelingToolkit.GeneratedFunctionWrap
per{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mt
k_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Modeling
Toolkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x5560ce01, 0x991a4cdf,
0x392020a7), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{
(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_Mod
Tag", ModelingToolkit.var"#_RGF_ModTag", (0x2b19e578, 0x47f62e68, 0x3f23a85
d, 0xb87b692a, 0xb5777171), Nothing}}}(ModelingToolkit.GeneratedFunctionWra
pper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__m
tk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Modelin
gToolkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x5560ce01, 0x991a4cdf
, 0x392020a7), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction
{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_Mo
dTag", ModelingToolkit.var"#_RGF_ModTag", (0x2b19e578, 0x47f62e68, 0x3f23a8
5d, 0xb87b692a, 0xb5777171), Nothing}}(RuntimeGeneratedFunctions.RuntimeGen
eratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_
RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x
5560ce01, 0x991a4cdf, 0x392020a7), Nothing}(nothing), RuntimeGeneratedFunct
ions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___),
ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x2
b19e578, 0x47f62e68, 0x3f23a85d, 0xb87b692a, 0xb5777171), Nothing}(nothing)
)), ModelingToolkit.var"#initprobpmap_split#810"{ModelingToolkit.var"#_gett
er#806"{Tuple{Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float
64}}}, ComposedFunction{ModelingToolkit.PConstructorApplicator{typeof(ident
ity)}, ModelingToolkit.ObservedWrapper{false, ModelingToolkit.GeneratedFunc
tionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunctio
n{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag",
ModelingToolkit.var"#_RGF_ModTag", (0x383e1f76, 0x30e3ca66, 0xe27ee296, 0x7
de466bf, 0xddedf6e9), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedF
unction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#
_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xdef1fe73, 0x41a6768b, 0
x43614868, 0x9db8eb5f, 0xb69f9719), Nothing}}}}, Returns{Tuple{}}, Returns{
Tuple{}}, Returns{Tuple{}}}}}(ModelingToolkit.var"#_getter#806"{Tuple{Retur
ns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}}, ComposedFunc
tion{ModelingToolkit.PConstructorApplicator{typeof(identity)}, ModelingTool
kit.ObservedWrapper{false, ModelingToolkit.GeneratedFunctionWrapper{(2, 2,
true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :_
__mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var
"#_RGF_ModTag", (0x383e1f76, 0x30e3ca66, 0xe27ee296, 0x7de466bf, 0xddedf6e9
), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :_
_mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Model
ingToolkit.var"#_RGF_ModTag", (0xdef1fe73, 0x41a6768b, 0x43614868, 0x9db8eb
5f, 0xb69f9719), Nothing}}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{T
uple{}}}}((Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}
}}(Float64[]), ModelingToolkit.PConstructorApplicator{typeof(identity)}(ide
ntity) ∘ ModelingToolkit.ObservedWrapper{false, ModelingToolkit.GeneratedFu
nctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunct
ion{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag"
, ModelingToolkit.var"#_RGF_ModTag", (0x383e1f76, 0x30e3ca66, 0xe27ee296, 0
x7de466bf, 0xddedf6e9), Nothing}, RuntimeGeneratedFunctions.RuntimeGenerate
dFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var
"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xdef1fe73, 0x41a6768b,
0x43614868, 0x9db8eb5f, 0xb69f9719), Nothing}}}(ModelingToolkit.GeneratedF
unctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunc
tion{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag
", ModelingToolkit.var"#_RGF_ModTag", (0x383e1f76, 0x30e3ca66, 0xe27ee296,
0x7de466bf, 0xddedf6e9), Nothing}, RuntimeGeneratedFunctions.RuntimeGenerat
edFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.va
r"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xdef1fe73, 0x41a6768b
, 0x43614868, 0x9db8eb5f, 0xb69f9719), Nothing}}(RuntimeGeneratedFunctions.
RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingTool
kit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x383e1f76, 0x30
e3ca66, 0xe27ee296, 0x7de466bf, 0xddedf6e9), Nothing}(nothing), RuntimeGene
ratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparam
eters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_Mod
Tag", (0xdef1fe73, 0x41a6768b, 0x43614868, 0x9db8eb5f, 0xb69f9719), Nothing
}(nothing))), Returns{Tuple{}}(()), Returns{Tuple{}}(()), Returns{Tuple{}}(
())))), ModelingToolkit.InitializationMetadata{ModelingToolkit.ReconstructI
nitializeprob{ModelingToolkit.var"#_getter#806"{Tuple{ComposedFunction{Mode
lingToolkit.PConstructorApplicator{typeof(identity)}, ModelingToolkit.Obser
vedWrapper{true, ModelingToolkit.GeneratedFunctionWrapper{(2, 3, true), Run
timeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparam
eters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF
_ModTag", (0x7e79da91, 0xd20b440a, 0x8f31de5e, 0xb3bf1671, 0x1e4c890d), Not
hing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_a
rg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", Modelin
gToolkit.var"#_RGF_ModTag", (0xdc0e8bfb, 0xe657b82a, 0x2b04a79c, 0xdd2049fc
, 0x2f912348), Nothing}}}}, Returns{StaticArraysCore.SizedVector{0, Float64
, Vector{Float64}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}
, ComposedFunction{typeof(identity), SymbolicIndexingInterface.TimeDependen
tObservedFunction{SymbolicIndexingInterface.ContinuousTimeseries, ModelingT
oolkit.GeneratedFunctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.Run
timeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToo
lkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe2dbe4c4, 0x8
637425f, 0xf9877c30, 0xc6a732b9, 0xb3aed46a), Nothing}, RuntimeGeneratedFun
ctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___
, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag"
, (0xc0ff0587, 0x8943b463, 0x759a7721, 0x55ab8be5, 0xe5da0c74), Nothing}},
true}}}, ModelingToolkit.GetUpdatedU0{SymbolicIndexingInterface.TimeIndepen
dentObservedFunction{ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true),
RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkp
arameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF
_ModTag", (0x402c48b5, 0xfa2314b8, 0x4a877dea, 0xd8553b68, 0xe8202d4a), Not
hing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_a
rg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToo
lkit.var"#_RGF_ModTag", (0xefb5629c, 0x6f14cbd6, 0xfff3a505, 0x6fdc0cc0, 0x
6dc034e6), Nothing}}}, SymbolicIndexingInterface.MultipleParametersGetter{S
ymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInter
face.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initi
als, Int64}}}, Nothing}}, ModelingToolkit.SetInitialUnknowns{SymbolicIndexi
ngInterface.MultipleSetters{Vector{SymbolicIndexingInterface.ParameterHookW
rapper{SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.Paramete
rIndex{SciMLStructures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}
}}}}}(Dict{Any, Any}(vφ2(t) => Initial(vφ2(t)), q₂(t) => Initial(q₂(t)), λ₂
(t) => Initial(λ₂(t)), vq₁(t) => Initial(vq₁(t)), vq₂(t) => Initial(vq₂(t))
, x₃(t) => Initial(x₃(t)), q₁(t) => Initial(q₁(t)), λ₁(t) => Initial(λ₁(t))
, q₃(t) => Initial(q₃(t)), vq₄(t) => Initial(vq₄(t))…), Dict{Any, Any}(Init
ial(vφ1ˍt(t)) => false, Initial(vφ1ˍtt(t)) => false, Initial(vq₄ˍt(t)) => f
alse, Initial(vx₃(t)) => -2.68938672e-6, Initial(λ₂(t)) => 382.458950952669
85, Initial(λ₂ˍt(t)) => false, Initial(q₄(t)) => 1.69327969e-5, Initial(vφ1
(t)) => 150.0, Initial(vx₃ˍt(t)) => false, Initial(x₃ˍtt(t)) => false…), Di
ct{Any, Any}(), Symbolics.Equation[], true, ModelingToolkit.ReconstructInit
ializeprob{ModelingToolkit.var"#_getter#806"{Tuple{ComposedFunction{Modelin
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eGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparamete
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dTag", (0x7e79da91, 0xd20b440a, 0x8f31de5e, 0xb3bf1671, 0x1e4c890d), Nothin
g}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_
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x2f912348), Nothing}}}}, Returns{StaticArraysCore.SizedVector{0, Float64, V
ector{Float64}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}, C
omposedFunction{typeof(identity), SymbolicIndexingInterface.TimeDependentOb
servedFunction{SymbolicIndexingInterface.ContinuousTimeseries, ModelingTool
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425f, 0xf9877c30, 0xc6a732b9, 0xb3aed46a), Nothing}, RuntimeGeneratedFuncti
ons.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :
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e}}}(ModelingToolkit.var"#_getter#806"{Tuple{ComposedFunction{ModelingToolk
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:t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag",
(0x7e79da91, 0xd20b440a, 0x8f31de5e, 0xb3bf1671, 0x1e4c890d), Nothing}, Ru
ntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :__
_mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.
var"#_RGF_ModTag", (0xdc0e8bfb, 0xe657b82a, 0x2b04a79c, 0xdd2049fc, 0x2f912
348), Nothing}}}}, Returns{StaticArraysCore.SizedVector{0, Float64, Vector{
Float64}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}((Modelin
gToolkit.PConstructorApplicator{typeof(identity)}(identity) ∘ ModelingToolk
it.ObservedWrapper{true, ModelingToolkit.GeneratedFunctionWrapper{(2, 3, tr
ue), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___
mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.v
ar"#_RGF_ModTag", (0x7e79da91, 0xd20b440a, 0x8f31de5e, 0xb3bf1671, 0x1e4c89
0d), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out,
:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag",
ModelingToolkit.var"#_RGF_ModTag", (0xdc0e8bfb, 0xe657b82a, 0x2b04a79c, 0x
dd2049fc, 0x2f912348), Nothing}}}(ModelingToolkit.GeneratedFunctionWrapper{
(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_ar
g_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", Modeling
Toolkit.var"#_RGF_ModTag", (0x7e79da91, 0xd20b440a, 0x8f31de5e, 0xb3bf1671,
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(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF
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4a79c, 0xdd2049fc, 0x2f912348), Nothing}}(RuntimeGeneratedFunctions.Runtime
GeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit
.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x7e79da91, 0xd20b4
40a, 0x8f31de5e, 0xb3bf1671, 0x1e4c890d), Nothing}(nothing), RuntimeGenerat
edFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparamete
rs___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_Mo
dTag", (0xdc0e8bfb, 0xe657b82a, 0x2b04a79c, 0xdd2049fc, 0x2f912348), Nothin
g}(nothing))), Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Floa
t64}}}(Float64[]), Returns{Tuple{}}(()), Returns{Tuple{}}(()), Returns{Tupl
e{}}(()))), identity ∘ SymbolicIndexingInterface.TimeDependentObservedFunct
ion{SymbolicIndexingInterface.ContinuousTimeseries, ModelingToolkit.Generat
edFunctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedF
unction{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF
_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe2dbe4c4, 0x8637425f, 0xf98
77c30, 0xc6a732b9, 0xb3aed46a), Nothing}, RuntimeGeneratedFunctions.Runtime
GeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), Modelin
gToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc0ff0587,
0x8943b463, 0x759a7721, 0x55ab8be5, 0xe5da0c74), Nothing}}, true}(Symbolic
IndexingInterface.ContinuousTimeseries(), ModelingToolkit.GeneratedFunction
Wrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:
__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag",
ModelingToolkit.var"#_RGF_ModTag", (0xe2dbe4c4, 0x8637425f, 0xf9877c30, 0xc
6a732b9, 0xb3aed46a), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedF
unction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.v
ar"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc0ff0587, 0x8943b46
3, 0x759a7721, 0x55ab8be5, 0xe5da0c74), Nothing}}(RuntimeGeneratedFunctions
.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), Modelin
gToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe2dbe4c4,
0x8637425f, 0xf9877c30, 0xc6a732b9, 0xb3aed46a), Nothing}(nothing), Runtim
eGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtk
parameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"
#_RGF_ModTag", (0xc0ff0587, 0x8943b463, 0x759a7721, 0x55ab8be5, 0xe5da0c74)
, Nothing}(nothing)))), ModelingToolkit.GetUpdatedU0{SymbolicIndexingInterf
ace.TimeIndependentObservedFunction{ModelingToolkit.GeneratedFunctionWrappe
r{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_
arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingTo
olkit.var"#_RGF_ModTag", (0x402c48b5, 0xfa2314b8, 0x4a877dea, 0xd8553b68, 0
xe8202d4a), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:
ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTa
g", ModelingToolkit.var"#_RGF_ModTag", (0xefb5629c, 0x6f14cbd6, 0xfff3a505,
0x6fdc0cc0, 0x6dc034e6), Nothing}}}, SymbolicIndexingInterface.MultiplePar
ametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{Symbol
icIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLS
tructures.Initials, Int64}}}, Nothing}}(Bool[0, 0, 0, 0, 0, 0, 0, 0, 1, 1,
0, 0, 1], SymbolicIndexingInterface.TimeIndependentObservedFunction{Modelin
gToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.R
untimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolk
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314b8, 0x4a877dea, 0xd8553b68, 0xe8202d4a), Nothing}, RuntimeGeneratedFunct
ions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___),
ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe
fb5629c, 0x6f14cbd6, 0xfff3a505, 0x6fdc0cc0, 0x6dc034e6), Nothing}}}(Modeli
ngToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.
RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingTool
kit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x402c48b5, 0xfa
2314b8, 0x4a877dea, 0xd8553b68, 0xe8202d4a), Nothing}, RuntimeGeneratedFunc
tions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___)
, ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x
efb5629c, 0x6f14cbd6, 0xfff3a505, 0x6fdc0cc0, 0x6dc034e6), Nothing}}(Runtim
eGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparamete
rs___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag
", (0x402c48b5, 0xfa2314b8, 0x4a877dea, 0xd8553b68, 0xe8202d4a), Nothing}(n
othing), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk
_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingT
oolkit.var"#_RGF_ModTag", (0xefb5629c, 0x6f14cbd6, 0xfff3a505, 0x6fdc0cc0,
0x6dc034e6), Nothing}(nothing))), SymbolicIndexingInterface.MultipleParamet
ersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIn
dexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStruc
tures.Initials, Int64}}}, Nothing}(SymbolicIndexingInterface.GetParameterIn
dex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}[Symbol
icIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLS
tructures.Initials, Int64}}(ModelingToolkit.ParameterIndex{SciMLStructures.
Initials, Int64}(SciMLStructures.Initials(), 23, false)), SymbolicIndexingI
nterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.I
nitials, Int64}}(ModelingToolkit.ParameterIndex{SciMLStructures.Initials, I
nt64}(SciMLStructures.Initials(), 7, false)), SymbolicIndexingInterface.Get
ParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int
64}}(ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}(SciMLS
tructures.Initials(), 20, false)), SymbolicIndexingInterface.GetParameterIn
dex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}(Modeli
ngToolkit.ParameterIndex{SciMLStructures.Initials, Int64}(SciMLStructures.I
nitials(), 24, false)), SymbolicIndexingInterface.GetParameterIndex{Modelin
gToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}(ModelingToolkit.P
arameterIndex{SciMLStructures.Initials, Int64}(SciMLStructures.Initials(),
12, false)), SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.Pa
rameterIndex{SciMLStructures.Initials, Int64}}(ModelingToolkit.ParameterInd
ex{SciMLStructures.Initials, Int64}(SciMLStructures.Initials(), 34, false))
, SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterInde
x{SciMLStructures.Initials, Int64}}(ModelingToolkit.ParameterIndex{SciMLStr
uctures.Initials, Int64}(SciMLStructures.Initials(), 32, false)), SymbolicI
ndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStru
ctures.Initials, Int64}}(ModelingToolkit.ParameterIndex{SciMLStructures.Ini
tials, Int64}(SciMLStructures.Initials(), 41, false)), SymbolicIndexingInte
rface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Init
ials, Int64}}(ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int6
4}(SciMLStructures.Initials(), 30, false)), SymbolicIndexingInterface.GetPa
rameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64
}}(ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}(SciMLStr
uctures.Initials(), 3, false)), SymbolicIndexingInterface.GetParameterIndex
{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}(ModelingT
oolkit.ParameterIndex{SciMLStructures.Initials, Int64}(SciMLStructures.Init
ials(), 28, false)), SymbolicIndexingInterface.GetParameterIndex{ModelingTo
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false)), SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.Param
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SciMLStructures.Initials, Int64}(SciMLStructures.Initials(), 27, false))],
nothing)), ModelingToolkit.SetInitialUnknowns{SymbolicIndexingInterface.Mul
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se)), Initial(vq₄(t))), SymbolicIndexingInterface.ParameterHookWrapper{Symb
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olicIndexingInterface.ParameterHookWrapper{SymbolicIndexingInterface.SetPar
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x{SciMLStructures.Initials, Int64}(SciMLStructures.Initials(), 24, false)),
Initial(vq₁(t))), SymbolicIndexingInterface.ParameterHookWrapper{SymbolicI
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ngInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructure
s.Initials, Int64}}(ModelingToolkit.ParameterIndex{SciMLStructures.Initials
, Int64}(SciMLStructures.Initials(), 12, false)), Initial(vq₃(t))), Symboli
cIndexingInterface.ParameterHookWrapper{SymbolicIndexingInterface.SetParame
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SymbolicUtils.BasicSymbolic{Real}}(SymbolicIndexingInterface.SetParameterIn
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ngToolkit.ParameterIndex{SciMLStructures.Initials, Int64}(SciMLStructures.I
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tial(q₂(t))), SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexi
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s.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}(SymbolicIndexingInt
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icUtils.BasicSymbolic{Real}}(SymbolicIndexingInterface.SetParameterIndex{Mo
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kit.ParameterIndex{SciMLStructures.Initials, Int64}(SciMLStructures.Initial
s(), 30, false)), Initial(φ2ˍt(t))), SymbolicIndexingInterface.ParameterHoo
kWrapper{SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.Parame
terIndex{SciMLStructures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Rea
l}}(SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.ParameterIn
dex{SciMLStructures.Initials, Int64}}(ModelingToolkit.ParameterIndex{SciMLS
tructures.Initials, Int64}(SciMLStructures.Initials(), 3, false)), Initial(
vq₄ˍt(t))), SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexing
Interface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.
Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}(SymbolicIndexingInter
face.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initi
als, Int64}}(ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64
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gInterface.ParameterHookWrapper{SymbolicIndexingInterface.SetParameterIndex
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Utils.BasicSymbolic{Real}}(SymbolicIndexingInterface.SetParameterIndex{Mode
lingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}(ModelingToolki
t.ParameterIndex{SciMLStructures.Initials, Int64}(SciMLStructures.Initials(
), 13, false)), Initial(λ₁(t))), SymbolicIndexingInterface.ParameterHookWra
pper{SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.ParameterI
ndex{SciMLStructures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}(
SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{
SciMLStructures.Initials, Int64}}(ModelingToolkit.ParameterIndex{SciMLStruc
tures.Initials, Int64}(SciMLStructures.Initials(), 27, false)), Initial(φ2ˍ
tt(t)))]))), Val{true}()), nothing), [[-2.68938672e-6, 1.69327969e-5, 0.004
63434311, 0.444896105, -1.78591076e-6, 0.0, 0.0, 1.03339863e-5, -74.9957670
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1, 0.44489610582496486, -6.054169572838606e-6, 4.4489610526360277e-7, 4.634
343115925256e-9, 1.0333982379911497e-5, -74.99576640815987, 0.2090849108295
245, -7.499576682940703e-5, 0.06633259074438658, 1.2644137075378408], [-1.5
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23231106, -2.632512031208655e-5, 2.561212442247891e-6, 2.6679346804030267e-
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f0ec1653, 0x15ca6ae7, 0xc592e306, 0xfafbb2ec, 0x9859bcb5), Nothing}, Runtim
eGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtk
parameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"
#_RGF_ModTag", (0x4661a20f, 0xc7cca64b, 0x7a70f6cf, 0x6d73e89a, 0xb0133243)
, Nothing}}}}(SciMLBase.Void{ModelingToolkit.GeneratedFunctionWrapper{(2, 3
, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1,
:___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolk
it.var"#_RGF_ModTag", (0xf0ec1653, 0x15ca6ae7, 0xc592e306, 0xfafbb2ec, 0x98
59bcb5), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋o
ut, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModT
ag", ModelingToolkit.var"#_RGF_ModTag", (0x4661a20f, 0xc7cca64b, 0x7a70f6cf
, 0x6d73e89a, 0xb0133243), Nothing}}}(ModelingToolkit.GeneratedFunctionWrap
per{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mt
k_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", Mode
lingToolkit.var"#_RGF_ModTag", (0xf0ec1653, 0x15ca6ae7, 0xc592e306, 0xfafbb
2ec, 0x9859bcb5), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunct
ion{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#
_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x4661a20f, 0xc7cca64b, 0
x7a70f6cf, 0x6d73e89a, 0xb0133243), Nothing}}(RuntimeGeneratedFunctions.Run
timeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToo
lkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xf0ec1653, 0x1
5ca6ae7, 0xc592e306, 0xfafbb2ec, 0x9859bcb5), Nothing}(nothing), RuntimeGen
eratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkpara
meters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RG
F_ModTag", (0x4661a20f, 0xc7cca64b, 0x7a70f6cf, 0x6d73e89a, 0xb0133243), No
thing}(nothing)))), SciMLBase.Void{ModelingToolkit.GeneratedFunctionWrapper
{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_a
rg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", Modelin
gToolkit.var"#_RGF_ModTag", (0xf0ec1653, 0x15ca6ae7, 0xc592e306, 0xfafbb2ec
, 0x9859bcb5), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction
{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RG
F_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x4661a20f, 0xc7cca64b, 0x7a
70f6cf, 0x6d73e89a, 0xb0133243), Nothing}}}))), [1.0 0.0 … 0.0 0.0; 0.0 1.0
… 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0], nothing, nothing, no
thing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothi
ng, nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.ODESyste
m}(Model sys:
Equations (13):
13 standard: see equations(sys)
Unknowns (13): see unknowns(sys)
vq₄(t) [defaults to -2.68939e-6]
q₄(t) [defaults to 1.69328e-5]
vq₂(t) [defaults to 0.00463434]
vq₁(t) [defaults to 0.444896]
⋮
Observed (14): see observed(sys), Dict{Any, Any}(), false, false, ModelingT
oolkit, false, true), nothing, Model sys:
Equations (13):
13 standard: see equations(sys)
Unknowns (13): see unknowns(sys)
vq₄(t) [defaults to -2.68939e-6]
q₄(t) [defaults to 1.69328e-5]
vq₂(t) [defaults to 0.00463434]
vq₁(t) [defaults to 0.444896]
⋮
Observed (14): see observed(sys), SciMLBase.OverrideInitData{SciMLBase.Nonl
inearLeastSquaresProblem{Vector{Float64}, true, ModelingToolkit.MTKParamete
rs{Vector{Float64}, StaticArraysCore.SizedVector{0, Float64, Vector{Float64
}}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, SciMLBase.NonlinearFunction{true,
SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionWrapper{(2, 2, t
rue), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :__
_mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"
#_RGF_ModTag", (0x855d74ab, 0xd2df28ae, 0xeb3ecdd0, 0x325306af, 0xd16f567f)
, Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__
mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Modeli
ngToolkit.var"#_RGF_ModTag", (0xc8a21f76, 0xd50266a8, 0x36ae5075, 0x4ece6d0
a, 0x4e546efd), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Not
hing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothin
g, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.NonlinearSystem},
Nothing, ModelingToolkit.NonlinearSystem, Vector{Float64}, Nothing}, Base.P
airs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, Nothing, Nothing}, typeof(Mo
delingToolkit.update_initializeprob!), ComposedFunction{ComposedFunction{ty
peof(identity), typeof(ModelingToolkit.safe_float)}, SymbolicIndexingInterf
ace.TimeIndependentObservedFunction{ModelingToolkit.GeneratedFunctionWrappe
r{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_
arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingTo
olkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x5560ce01, 0x991a4cdf, 0
x392020a7), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:
ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTa
g", ModelingToolkit.var"#_RGF_ModTag", (0x2b19e578, 0x47f62e68, 0x3f23a85d,
0xb87b692a, 0xb5777171), Nothing}}}}, ModelingToolkit.var"#initprobpmap_sp
lit#810"{ModelingToolkit.var"#_getter#806"{Tuple{Returns{StaticArraysCore.S
izedVector{0, Float64, Vector{Float64}}}, ComposedFunction{ModelingToolkit.
PConstructorApplicator{typeof(identity)}, ModelingToolkit.ObservedWrapper{f
alse, ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGenerat
edFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___),
ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x38
3e1f76, 0x30e3ca66, 0xe27ee296, 0x7de466bf, 0xddedf6e9), Nothing}, RuntimeG
eneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkpa
rameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_
ModTag", (0xdef1fe73, 0x41a6768b, 0x43614868, 0x9db8eb5f, 0xb69f9719), Noth
ing}}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}}, ModelingT
oolkit.InitializationMetadata{ModelingToolkit.ReconstructInitializeprob{Mod
elingToolkit.var"#_getter#806"{Tuple{ComposedFunction{ModelingToolkit.PCons
tructorApplicator{typeof(identity)}, ModelingToolkit.ObservedWrapper{true,
ModelingToolkit.GeneratedFunctionWrapper{(2, 3, true), RuntimeGeneratedFunc
tions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), Mo
delingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x7e79
da91, 0xd20b440a, 0x8f31de5e, 0xb3bf1671, 0x1e4c890d), Nothing}, RuntimeGen
eratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkpara
meters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RG
F_ModTag", (0xdc0e8bfb, 0xe657b82a, 0x2b04a79c, 0xdd2049fc, 0x2f912348), No
thing}}}}, Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}
}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}, ComposedFunctio
n{typeof(identity), SymbolicIndexingInterface.TimeDependentObservedFunction
{SymbolicIndexingInterface.ContinuousTimeseries, ModelingToolkit.GeneratedF
unctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunc
tion{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_Mo
dTag", ModelingToolkit.var"#_RGF_ModTag", (0xe2dbe4c4, 0x8637425f, 0xf9877c
30, 0xc6a732b9, 0xb3aed46a), Nothing}, RuntimeGeneratedFunctions.RuntimeGen
eratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingTo
olkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc0ff0587, 0x
8943b463, 0x759a7721, 0x55ab8be5, 0xe5da0c74), Nothing}}, true}}}, Modeling
Toolkit.GetUpdatedU0{SymbolicIndexingInterface.TimeIndependentObservedFunct
ion{ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGenerated
Functions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), Mo
delingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x402c
48b5, 0xfa2314b8, 0x4a877dea, 0xd8553b68, 0xe8202d4a), Nothing}, RuntimeGen
eratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkpara
meters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_Mo
dTag", (0xefb5629c, 0x6f14cbd6, 0xfff3a505, 0x6fdc0cc0, 0x6dc034e6), Nothin
g}}}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingIn
terface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameter
Index{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}}, No
thing}}, ModelingToolkit.SetInitialUnknowns{SymbolicIndexingInterface.Multi
pleSetters{Vector{SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIn
dexingInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStruc
tures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}}}}}, Val{true}}
(SciMLBase.NonlinearLeastSquaresProblem{Vector{Float64}, true, ModelingTool
kit.MTKParameters{Vector{Float64}, StaticArraysCore.SizedVector{0, Float64,
Vector{Float64}}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, SciMLBase.Nonlinear
Function{true, SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionW
rapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:_
_mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Model
ingToolkit.var"#_RGF_ModTag", (0x855d74ab, 0xd2df28ae, 0xeb3ecdd0, 0x325306
af, 0xd16f567f), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFuncti
on{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_
ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc8a21f76, 0xd50266a8, 0x36ae
5075, 0x4ece6d0a, 0x4e546efd), Nothing}}, LinearAlgebra.UniformScaling{Bool
}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing,
Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.Non
linearSystem}, Nothing, ModelingToolkit.NonlinearSystem, Vector{Float64}, N
othing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, Nothing, Noth
ing}(SciMLBase.NonlinearFunction{true, SciMLBase.FullSpecialize, ModelingTo
olkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.Runt
imeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.
var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x855d74ab, 0xd2df28
ae, 0xeb3ecdd0, 0x325306af, 0xd16f567f), Nothing}, RuntimeGeneratedFunction
s.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), Mo
delingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc8a2
1f76, 0xd50266a8, 0x36ae5075, 0x4ece6d0a, 0x4e546efd), Nothing}}, LinearAlg
ebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Not
hing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionC
ache{ModelingToolkit.NonlinearSystem}, Nothing, ModelingToolkit.NonlinearSy
stem, Vector{Float64}, Nothing}(ModelingToolkit.GeneratedFunctionWrapper{(2
, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_
1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolki
t.var"#_RGF_ModTag", (0x855d74ab, 0xd2df28ae, 0xeb3ecdd0, 0x325306af, 0xd16
f567f), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋ou
t, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag",
ModelingToolkit.var"#_RGF_ModTag", (0xc8a21f76, 0xd50266a8, 0x36ae5075, 0x4
ece6d0a, 0x4e546efd), Nothing}}(RuntimeGeneratedFunctions.RuntimeGeneratedF
unction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_Mod
Tag", ModelingToolkit.var"#_RGF_ModTag", (0x855d74ab, 0xd2df28ae, 0xeb3ecdd
0, 0x325306af, 0xd16f567f), Nothing}(nothing), RuntimeGeneratedFunctions.Ru
ntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), Modeli
ngToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc8a21f76
, 0xd50266a8, 0x36ae5075, 0x4ece6d0a, 0x4e546efd), Nothing}(nothing)), Line
arAlgebra.UniformScaling{Bool}(true), nothing, nothing, nothing, nothing, n
othing, nothing, nothing, nothing, nothing, nothing, ModelingToolkit.Observ
edFunctionCache{ModelingToolkit.NonlinearSystem}(Model sys:
Equations (10):
10 standard: see equations(sys)
Unknowns (1): see unknowns(sys)
vφ2ˍt(t) [defaults to -74.9958]
Parameters (45): see parameters(sys)
t
Initial(vφ1ˍt(t)) [defaults to false]
Initial(vφ1ˍtt(t)) [defaults to false]
Initial(vq₄ˍt(t)) [defaults to false]
⋮
Observed (26): see observed(sys), Dict{Any, Any}(SymbolicUtils.BasicSymboli
c{Real}[vq₄(t), q₄(t), vq₂(t), vq₁(t), vq₃(t), q₁(t), q₂(t), q₃(t), φ2ˍt(t)
, vq₄ˍt(t), φ2(t), λ₁(t), φ2ˍtt(t)] => ModelingToolkit.GeneratedFunctionWra
pper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__m
tk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Modelin
gToolkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x5560ce01, 0x991a4cdf
, 0x392020a7), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction
{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_Mo
dTag", ModelingToolkit.var"#_RGF_ModTag", (0x2b19e578, 0x47f62e68, 0x3f23a8
5d, 0xb87b692a, 0xb5777171), Nothing}}(RuntimeGeneratedFunctions.RuntimeGen
eratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_
RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x
5560ce01, 0x991a4cdf, 0x392020a7), Nothing}(nothing), RuntimeGeneratedFunct
ions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___),
ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x2
b19e578, 0x47f62e68, 0x3f23a85d, 0xb87b692a, 0xb5777171), Nothing}(nothing)
), Any[vq₄ˍt(t), φ2ˍtt(t), φ2ˍt(t)] => ModelingToolkit.GeneratedFunctionWra
pper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__m
tk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Modelin
gToolkit.var"#_RGF_ModTag", (0x59806009, 0x122eca51, 0xd6164a75, 0x9414c9c0
, 0xe211bcbc), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction
{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_Mo
dTag", ModelingToolkit.var"#_RGF_ModTag", (0x44b04ca3, 0xf8eac98b, 0x8198dd
8b, 0xa7a5108c, 0x9f72ce11), Nothing}}(RuntimeGeneratedFunctions.RuntimeGen
eratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_
RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x59806009, 0x122eca51, 0x
d6164a75, 0x9414c9c0, 0xe211bcbc), Nothing}(nothing), RuntimeGeneratedFunct
ions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___),
ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x4
4b04ca3, 0xf8eac98b, 0x8198dd8b, 0xa7a5108c, 0x9f72ce11), Nothing}(nothing)
)), false, false, ModelingToolkit, false, true), nothing, Model sys:
Equations (10):
10 standard: see equations(sys)
Unknowns (1): see unknowns(sys)
vφ2ˍt(t) [defaults to -74.9958]
Parameters (45): see parameters(sys)
t
Initial(vφ1ˍt(t)) [defaults to false]
Initial(vφ1ˍtt(t)) [defaults to false]
Initial(vq₄ˍt(t)) [defaults to false]
⋮
Observed (26): see observed(sys), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0], nothing), [0.0], ModelingToolkit.MTKParameters{Vector{Float64},
StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}, Tuple{}, Tuple{}
, Tuple{}, Tuple{}}([0.0, 0.0, 0.0, 0.0, -2.68938672e-6, 382.45895095266985
, 0.0, 1.69327969e-5, 150.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.033398
63e-5, 0.0, 0.0, 0.0], Float64[], (), (), (), ()), nothing, nothing, Base.P
airs{Symbol, Union{}, Tuple{}, @NamedTuple{}}()), ModelingToolkit.update_in
itializeprob!, identity ∘ ModelingToolkit.safe_float ∘ SymbolicIndexingInte
rface.TimeIndependentObservedFunction{ModelingToolkit.GeneratedFunctionWrap
per{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mt
k_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Modeling
Toolkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x5560ce01, 0x991a4cdf,
0x392020a7), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{
(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_Mod
Tag", ModelingToolkit.var"#_RGF_ModTag", (0x2b19e578, 0x47f62e68, 0x3f23a85
d, 0xb87b692a, 0xb5777171), Nothing}}}(ModelingToolkit.GeneratedFunctionWra
pper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__m
tk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Modelin
gToolkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x5560ce01, 0x991a4cdf
, 0x392020a7), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction
{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_Mo
dTag", ModelingToolkit.var"#_RGF_ModTag", (0x2b19e578, 0x47f62e68, 0x3f23a8
5d, 0xb87b692a, 0xb5777171), Nothing}}(RuntimeGeneratedFunctions.RuntimeGen
eratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_
RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x
5560ce01, 0x991a4cdf, 0x392020a7), Nothing}(nothing), RuntimeGeneratedFunct
ions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___),
ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x2
b19e578, 0x47f62e68, 0x3f23a85d, 0xb87b692a, 0xb5777171), Nothing}(nothing)
)), ModelingToolkit.var"#initprobpmap_split#810"{ModelingToolkit.var"#_gett
er#806"{Tuple{Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float
64}}}, ComposedFunction{ModelingToolkit.PConstructorApplicator{typeof(ident
ity)}, ModelingToolkit.ObservedWrapper{false, ModelingToolkit.GeneratedFunc
tionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunctio
n{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag",
ModelingToolkit.var"#_RGF_ModTag", (0x383e1f76, 0x30e3ca66, 0xe27ee296, 0x7
de466bf, 0xddedf6e9), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedF
unction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#
_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xdef1fe73, 0x41a6768b, 0
x43614868, 0x9db8eb5f, 0xb69f9719), Nothing}}}}, Returns{Tuple{}}, Returns{
Tuple{}}, Returns{Tuple{}}}}}(ModelingToolkit.var"#_getter#806"{Tuple{Retur
ns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}}, ComposedFunc
tion{ModelingToolkit.PConstructorApplicator{typeof(identity)}, ModelingTool
kit.ObservedWrapper{false, ModelingToolkit.GeneratedFunctionWrapper{(2, 2,
true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :_
__mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var
"#_RGF_ModTag", (0x383e1f76, 0x30e3ca66, 0xe27ee296, 0x7de466bf, 0xddedf6e9
), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :_
_mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Model
ingToolkit.var"#_RGF_ModTag", (0xdef1fe73, 0x41a6768b, 0x43614868, 0x9db8eb
5f, 0xb69f9719), Nothing}}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{T
uple{}}}}((Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}
}}(Float64[]), ModelingToolkit.PConstructorApplicator{typeof(identity)}(ide
ntity) ∘ ModelingToolkit.ObservedWrapper{false, ModelingToolkit.GeneratedFu
nctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunct
ion{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag"
, ModelingToolkit.var"#_RGF_ModTag", (0x383e1f76, 0x30e3ca66, 0xe27ee296, 0
x7de466bf, 0xddedf6e9), Nothing}, RuntimeGeneratedFunctions.RuntimeGenerate
dFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var
"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xdef1fe73, 0x41a6768b,
0x43614868, 0x9db8eb5f, 0xb69f9719), Nothing}}}(ModelingToolkit.GeneratedF
unctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunc
tion{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag
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edFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.va
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, 0x43614868, 0x9db8eb5f, 0xb69f9719), Nothing}}(RuntimeGeneratedFunctions.
RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingTool
kit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x383e1f76, 0x30
e3ca66, 0xe27ee296, 0x7de466bf, 0xddedf6e9), Nothing}(nothing), RuntimeGene
ratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparam
eters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_Mod
Tag", (0xdef1fe73, 0x41a6768b, 0x43614868, 0x9db8eb5f, 0xb69f9719), Nothing
}(nothing))), Returns{Tuple{}}(()), Returns{Tuple{}}(()), Returns{Tuple{}}(
())))), ModelingToolkit.InitializationMetadata{ModelingToolkit.ReconstructI
nitializeprob{ModelingToolkit.var"#_getter#806"{Tuple{ComposedFunction{Mode
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hing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_a
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, Vector{Float64}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}
, ComposedFunction{typeof(identity), SymbolicIndexingInterface.TimeDependen
tObservedFunction{SymbolicIndexingInterface.ContinuousTimeseries, ModelingT
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lkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe2dbe4c4, 0x8
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true}}}, ModelingToolkit.GetUpdatedU0{SymbolicIndexingInterface.TimeIndepen
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RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkp
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ymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInter
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als, Int64}}}, Nothing}}, ModelingToolkit.SetInitialUnknowns{SymbolicIndexi
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, x₃(t) => Initial(x₃(t)), q₁(t) => Initial(q₁(t)), λ₁(t) => Initial(λ₁(t))
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g}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_
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servedFunction{SymbolicIndexingInterface.ContinuousTimeseries, ModelingTool
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:t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag",
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ntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :__
_mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.
var"#_RGF_ModTag", (0xdc0e8bfb, 0xe657b82a, 0x2b04a79c, 0xdd2049fc, 0x2f912
348), Nothing}}}}, Returns{StaticArraysCore.SizedVector{0, Float64, Vector{
Float64}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}((Modelin
gToolkit.PConstructorApplicator{typeof(identity)}(identity) ∘ ModelingToolk
it.ObservedWrapper{true, ModelingToolkit.GeneratedFunctionWrapper{(2, 3, tr
ue), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___
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0d), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out,
:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag",
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dd2049fc, 0x2f912348), Nothing}}}(ModelingToolkit.GeneratedFunctionWrapper{
(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_ar
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Toolkit.var"#_RGF_ModTag", (0x7e79da91, 0xd20b440a, 0x8f31de5e, 0xb3bf1671,
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(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF
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4a79c, 0xdd2049fc, 0x2f912348), Nothing}}(RuntimeGeneratedFunctions.Runtime
GeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit
.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x7e79da91, 0xd20b4
40a, 0x8f31de5e, 0xb3bf1671, 0x1e4c890d), Nothing}(nothing), RuntimeGenerat
edFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparamete
rs___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_Mo
dTag", (0xdc0e8bfb, 0xe657b82a, 0x2b04a79c, 0xdd2049fc, 0x2f912348), Nothin
g}(nothing))), Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Floa
t64}}}(Float64[]), Returns{Tuple{}}(()), Returns{Tuple{}}(()), Returns{Tupl
e{}}(()))), identity ∘ SymbolicIndexingInterface.TimeDependentObservedFunct
ion{SymbolicIndexingInterface.ContinuousTimeseries, ModelingToolkit.Generat
edFunctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedF
unction{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF
_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe2dbe4c4, 0x8637425f, 0xf98
77c30, 0xc6a732b9, 0xb3aed46a), Nothing}, RuntimeGeneratedFunctions.Runtime
GeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), Modelin
gToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc0ff0587,
0x8943b463, 0x759a7721, 0x55ab8be5, 0xe5da0c74), Nothing}}, true}(Symbolic
IndexingInterface.ContinuousTimeseries(), ModelingToolkit.GeneratedFunction
Wrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:
__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag",
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6a732b9, 0xb3aed46a), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedF
unction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.v
ar"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc0ff0587, 0x8943b46
3, 0x759a7721, 0x55ab8be5, 0xe5da0c74), Nothing}}(RuntimeGeneratedFunctions
.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), Modelin
gToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe2dbe4c4,
0x8637425f, 0xf9877c30, 0xc6a732b9, 0xb3aed46a), Nothing}(nothing), Runtim
eGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtk
parameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"
#_RGF_ModTag", (0xc0ff0587, 0x8943b463, 0x759a7721, 0x55ab8be5, 0xe5da0c74)
, Nothing}(nothing)))), ModelingToolkit.GetUpdatedU0{SymbolicIndexingInterf
ace.TimeIndependentObservedFunction{ModelingToolkit.GeneratedFunctionWrappe
r{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_
arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingTo
olkit.var"#_RGF_ModTag", (0x402c48b5, 0xfa2314b8, 0x4a877dea, 0xd8553b68, 0
xe8202d4a), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:
ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTa
g", ModelingToolkit.var"#_RGF_ModTag", (0xefb5629c, 0x6f14cbd6, 0xfff3a505,
0x6fdc0cc0, 0x6dc034e6), Nothing}}}, SymbolicIndexingInterface.MultiplePar
ametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{Symbol
icIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLS
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0, 0, 1], SymbolicIndexingInterface.TimeIndependentObservedFunction{Modelin
gToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.R
untimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolk
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314b8, 0x4a877dea, 0xd8553b68, 0xe8202d4a), Nothing}, RuntimeGeneratedFunct
ions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___),
ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe
fb5629c, 0x6f14cbd6, 0xfff3a505, 0x6fdc0cc0, 0x6dc034e6), Nothing}}}(Modeli
ngToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.
RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingTool
kit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x402c48b5, 0xfa
2314b8, 0x4a877dea, 0xd8553b68, 0xe8202d4a), Nothing}, RuntimeGeneratedFunc
tions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___)
, ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x
efb5629c, 0x6f14cbd6, 0xfff3a505, 0x6fdc0cc0, 0x6dc034e6), Nothing}}(Runtim
eGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparamete
rs___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag
", (0x402c48b5, 0xfa2314b8, 0x4a877dea, 0xd8553b68, 0xe8202d4a), Nothing}(n
othing), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk
_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingT
oolkit.var"#_RGF_ModTag", (0xefb5629c, 0x6f14cbd6, 0xfff3a505, 0x6fdc0cc0,
0x6dc034e6), Nothing}(nothing))), SymbolicIndexingInterface.MultipleParamet
ersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIn
dexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStruc
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Initials, Int64}(SciMLStructures.Initials(), 23, false)), SymbolicIndexingI
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nitials, Int64}}(ModelingToolkit.ParameterIndex{SciMLStructures.Initials, I
nt64}(SciMLStructures.Initials(), 7, false)), SymbolicIndexingInterface.Get
ParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int
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tructures.Initials(), 20, false)), SymbolicIndexingInterface.GetParameterIn
dex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}(Modeli
ngToolkit.ParameterIndex{SciMLStructures.Initials, Int64}(SciMLStructures.I
nitials(), 24, false)), SymbolicIndexingInterface.GetParameterIndex{Modelin
gToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}(ModelingToolkit.P
arameterIndex{SciMLStructures.Initials, Int64}(SciMLStructures.Initials(),
12, false)), SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.Pa
rameterIndex{SciMLStructures.Initials, Int64}}(ModelingToolkit.ParameterInd
ex{SciMLStructures.Initials, Int64}(SciMLStructures.Initials(), 34, false))
, SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterInde
x{SciMLStructures.Initials, Int64}}(ModelingToolkit.ParameterIndex{SciMLStr
uctures.Initials, Int64}(SciMLStructures.Initials(), 32, false)), SymbolicI
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tials, Int64}(SciMLStructures.Initials(), 41, false)), SymbolicIndexingInte
rface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Init
ials, Int64}}(ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int6
4}(SciMLStructures.Initials(), 30, false)), SymbolicIndexingInterface.GetPa
rameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64
}}(ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}(SciMLStr
uctures.Initials(), 3, false)), SymbolicIndexingInterface.GetParameterIndex
{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}(ModelingT
oolkit.ParameterIndex{SciMLStructures.Initials, Int64}(SciMLStructures.Init
ials(), 28, false)), SymbolicIndexingInterface.GetParameterIndex{ModelingTo
olkit.ParameterIndex{SciMLStructures.Initials, Int64}}(ModelingToolkit.Para
meterIndex{SciMLStructures.Initials, Int64}(SciMLStructures.Initials(), 13,
false)), SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.Param
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SciMLStructures.Initials, Int64}(SciMLStructures.Initials(), 27, false))],
nothing)), ModelingToolkit.SetInitialUnknowns{SymbolicIndexingInterface.Mul
tipleSetters{Vector{SymbolicIndexingInterface.ParameterHookWrapper{Symbolic
IndexingInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStr
uctures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}}}}(SymbolicIn
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ookWrapper{SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.Para
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eal}}}}(SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexingInte
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.ParameterHookWrapper{SymbolicIndexingInterface.SetParameterIndex{ModelingT
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se)), Initial(vq₄(t))), SymbolicIndexingInterface.ParameterHookWrapper{Symb
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LStructures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}(SymbolicI
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olicIndexingInterface.ParameterHookWrapper{SymbolicIndexingInterface.SetPar
ameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}
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olic{Real}}(SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.Par
ameterIndex{SciMLStructures.Initials, Int64}}(ModelingToolkit.ParameterInde
x{SciMLStructures.Initials, Int64}(SciMLStructures.Initials(), 24, false)),
Initial(vq₁(t))), SymbolicIndexingInterface.ParameterHookWrapper{SymbolicI
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ctures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}(SymbolicIndexi
ngInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructure
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, Int64}(SciMLStructures.Initials(), 12, false)), Initial(vq₃(t))), Symboli
cIndexingInterface.ParameterHookWrapper{SymbolicIndexingInterface.SetParame
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SymbolicUtils.BasicSymbolic{Real}}(SymbolicIndexingInterface.SetParameterIn
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ngToolkit.ParameterIndex{SciMLStructures.Initials, Int64}(SciMLStructures.I
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rHookWrapper{SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.Pa
rameterIndex{SciMLStructures.Initials, Int64}}, SymbolicUtils.BasicSymbolic
{Real}}(SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.Paramet
erIndex{SciMLStructures.Initials, Int64}}(ModelingToolkit.ParameterIndex{Sc
iMLStructures.Initials, Int64}(SciMLStructures.Initials(), 32, false)), Ini
tial(q₂(t))), SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexi
ngInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructure
s.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}(SymbolicIndexingInt
erface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Ini
tials, Int64}}(ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int
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ingInterface.ParameterHookWrapper{SymbolicIndexingInterface.SetParameterInd
ex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}, Symbol
icUtils.BasicSymbolic{Real}}(SymbolicIndexingInterface.SetParameterIndex{Mo
delingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}(ModelingTool
kit.ParameterIndex{SciMLStructures.Initials, Int64}(SciMLStructures.Initial
s(), 30, false)), Initial(φ2ˍt(t))), SymbolicIndexingInterface.ParameterHoo
kWrapper{SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.Parame
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Nothing}(nothing)))), SciMLBase.Void{ModelingToolkit.GeneratedFunctionWrap
per{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mt
k_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", Mode
lingToolkit.var"#_RGF_ModTag", (0xf0ec1653, 0x15ca6ae7, 0xc592e306, 0xfafbb
2ec, 0x9859bcb5), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunct
ion{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#
_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x4661a20f, 0xc7cca64b, 0
x7a70f6cf, 0x6d73e89a, 0xb0133243), Nothing}}}), FunctionWrappers.FunctionW
rapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.Or
dinaryDiffEqTag, Float64}, Float64, 1}}, Vector{ForwardDiff.Dual{ForwardDif
f.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, ModelingToolkit
.MTKParameters{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}, V
ector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, Float64}}(Ptr{Nothing}
@0x00007f7153c52b50, Ptr{Nothing} @0x00007f719c998058, Base.RefValue{SciML
Base.Void{ModelingToolkit.GeneratedFunctionWrapper{(2, 3, true), RuntimeGen
eratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters__
_, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag
", (0xf0ec1653, 0x15ca6ae7, 0xc592e306, 0xfafbb2ec, 0x9859bcb5), Nothing},
RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :
___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolki
t.var"#_RGF_ModTag", (0x4661a20f, 0xc7cca64b, 0x7a70f6cf, 0x6d73e89a, 0xb01
33243), Nothing}}}}(SciMLBase.Void{ModelingToolkit.GeneratedFunctionWrapper
{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_a
rg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", Modelin
gToolkit.var"#_RGF_ModTag", (0xf0ec1653, 0x15ca6ae7, 0xc592e306, 0xfafbb2ec
, 0x9859bcb5), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction
{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RG
F_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x4661a20f, 0xc7cca64b, 0x7a
70f6cf, 0x6d73e89a, 0xb0133243), Nothing}}}(ModelingToolkit.GeneratedFuncti
onWrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{
(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag"
, ModelingToolkit.var"#_RGF_ModTag", (0xf0ec1653, 0x15ca6ae7, 0xc592e306, 0
xfafbb2ec, 0x9859bcb5), Nothing}, RuntimeGeneratedFunctions.RuntimeGenerate
dFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit
.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x4661a20f, 0xc7cca
64b, 0x7a70f6cf, 0x6d73e89a, 0xb0133243), Nothing}}(RuntimeGeneratedFunctio
ns.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), Model
ingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xf0ec165
3, 0x15ca6ae7, 0xc592e306, 0xfafbb2ec, 0x9859bcb5), Nothing}(nothing), Runt
imeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___m
tkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.va
r"#_RGF_ModTag", (0x4661a20f, 0xc7cca64b, 0x7a70f6cf, 0x6d73e89a, 0xb013324
3), Nothing}(nothing)))), SciMLBase.Void{ModelingToolkit.GeneratedFunctionW
rapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:_
_mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", M
odelingToolkit.var"#_RGF_ModTag", (0xf0ec1653, 0x15ca6ae7, 0xc592e306, 0xfa
fbb2ec, 0x9859bcb5), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFu
nction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.va
r"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x4661a20f, 0xc7cca64b
, 0x7a70f6cf, 0x6d73e89a, 0xb0133243), Nothing}}}), FunctionWrappers.Functi
onWrapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase
.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Vector{Float64}, ModelingToolki
t.MTKParameters{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}},
Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, ForwardDiff.Dual{Forw
ardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}}(Ptr{Nothi
ng} @0x00007f7153c53e70, Ptr{Nothing} @0x00007f719c9980a8, Base.RefValue{Sc
iMLBase.Void{ModelingToolkit.GeneratedFunctionWrapper{(2, 3, true), Runtime
GeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameter
s___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_Mod
Tag", (0xf0ec1653, 0x15ca6ae7, 0xc592e306, 0xfafbb2ec, 0x9859bcb5), Nothing
}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1
, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToo
lkit.var"#_RGF_ModTag", (0x4661a20f, 0xc7cca64b, 0x7a70f6cf, 0x6d73e89a, 0x
b0133243), Nothing}}}}(SciMLBase.Void{ModelingToolkit.GeneratedFunctionWrap
per{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mt
k_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", Mode
lingToolkit.var"#_RGF_ModTag", (0xf0ec1653, 0x15ca6ae7, 0xc592e306, 0xfafbb
2ec, 0x9859bcb5), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunct
ion{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#
_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x4661a20f, 0xc7cca64b, 0
x7a70f6cf, 0x6d73e89a, 0xb0133243), Nothing}}}(ModelingToolkit.GeneratedFun
ctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFuncti
on{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModT
ag", ModelingToolkit.var"#_RGF_ModTag", (0xf0ec1653, 0x15ca6ae7, 0xc592e306
, 0xfafbb2ec, 0x9859bcb5), Nothing}, RuntimeGeneratedFunctions.RuntimeGener
atedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingTool
kit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x4661a20f, 0xc7
cca64b, 0x7a70f6cf, 0x6d73e89a, 0xb0133243), Nothing}}(RuntimeGeneratedFunc
tions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), Mo
delingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xf0ec
1653, 0x15ca6ae7, 0xc592e306, 0xfafbb2ec, 0x9859bcb5), Nothing}(nothing), R
untimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :_
__mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit
.var"#_RGF_ModTag", (0x4661a20f, 0xc7cca64b, 0x7a70f6cf, 0x6d73e89a, 0xb013
3243), Nothing}(nothing)))), SciMLBase.Void{ModelingToolkit.GeneratedFuncti
onWrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{
(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag"
, ModelingToolkit.var"#_RGF_ModTag", (0xf0ec1653, 0x15ca6ae7, 0xc592e306, 0
xfafbb2ec, 0x9859bcb5), Nothing}, RuntimeGeneratedFunctions.RuntimeGenerate
dFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit
.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x4661a20f, 0xc7cca
64b, 0x7a70f6cf, 0x6d73e89a, 0xb0133243), Nothing}}}), FunctionWrappers.Fun
ctionWrapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqB
ase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Vector{ForwardDiff.Dual{Forw
ardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, ModelingT
oolkit.MTKParameters{StaticArraysCore.SizedVector{0, Float64, Vector{Float6
4}}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, ForwardDiff.Dual
{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}}(Ptr{
Nothing} @0x00007f7153c55dc0, Ptr{Nothing} @0x00007f719c9980d0, Base.RefVal
ue{SciMLBase.Void{ModelingToolkit.GeneratedFunctionWrapper{(2, 3, true), Ru
ntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkpara
meters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RG
F_ModTag", (0xf0ec1653, 0x15ca6ae7, 0xc592e306, 0xfafbb2ec, 0x9859bcb5), No
thing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_
arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", Modeli
ngToolkit.var"#_RGF_ModTag", (0x4661a20f, 0xc7cca64b, 0x7a70f6cf, 0x6d73e89
a, 0xb0133243), Nothing}}}}(SciMLBase.Void{ModelingToolkit.GeneratedFunctio
nWrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(
:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag",
ModelingToolkit.var"#_RGF_ModTag", (0xf0ec1653, 0x15ca6ae7, 0xc592e306, 0x
fafbb2ec, 0x9859bcb5), Nothing}, RuntimeGeneratedFunctions.RuntimeGenerated
Function{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.
var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x4661a20f, 0xc7cca6
4b, 0x7a70f6cf, 0x6d73e89a, 0xb0133243), Nothing}}}(ModelingToolkit.Generat
edFunctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedF
unction{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF
_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xf0ec1653, 0x15ca6ae7, 0xc59
2e306, 0xfafbb2ec, 0x9859bcb5), Nothing}, RuntimeGeneratedFunctions.Runtime
GeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), Modelin
gToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x4661a20f,
0xc7cca64b, 0x7a70f6cf, 0x6d73e89a, 0xb0133243), Nothing}}(RuntimeGenerate
dFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t
), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0
xf0ec1653, 0x15ca6ae7, 0xc592e306, 0xfafbb2ec, 0x9859bcb5), Nothing}(nothin
g), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_
1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingTo
olkit.var"#_RGF_ModTag", (0x4661a20f, 0xc7cca64b, 0x7a70f6cf, 0x6d73e89a, 0
xb0133243), Nothing}(nothing)))), SciMLBase.Void{ModelingToolkit.GeneratedF
unctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunc
tion{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_Mo
dTag", ModelingToolkit.var"#_RGF_ModTag", (0xf0ec1653, 0x15ca6ae7, 0xc592e3
06, 0xfafbb2ec, 0x9859bcb5), Nothing}, RuntimeGeneratedFunctions.RuntimeGen
eratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingTo
olkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x4661a20f, 0x
c7cca64b, 0x7a70f6cf, 0x6d73e89a, 0xb0133243), Nothing}}}))), [1.0 0.0 … 0.
0 0.0; 0.0 1.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0], nothin
g, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing,
nothing, nothing, nothing, ModelingToolkit.ObservedFunctionCache{ModelingTo
olkit.ODESystem}(Model sys:
Equations (13):
13 standard: see equations(sys)
Unknowns (13): see unknowns(sys)
vq₄(t) [defaults to -2.68939e-6]
q₄(t) [defaults to 1.69328e-5]
vq₂(t) [defaults to 0.00463434]
vq₁(t) [defaults to 0.444896]
⋮
Observed (14): see observed(sys), Dict{Any, Any}(), false, false, ModelingT
oolkit, false, true), nothing, Model sys:
Equations (13):
13 standard: see equations(sys)
Unknowns (13): see unknowns(sys)
vq₄(t) [defaults to -2.68939e-6]
q₄(t) [defaults to 1.69328e-5]
vq₂(t) [defaults to 0.00463434]
vq₁(t) [defaults to 0.444896]
⋮
Observed (14): see observed(sys), SciMLBase.OverrideInitData{SciMLBase.Nonl
inearLeastSquaresProblem{Vector{Float64}, true, ModelingToolkit.MTKParamete
rs{Vector{Float64}, StaticArraysCore.SizedVector{0, Float64, Vector{Float64
}}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, SciMLBase.NonlinearFunction{true,
SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionWrapper{(2, 2, t
rue), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :__
_mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"
#_RGF_ModTag", (0x855d74ab, 0xd2df28ae, 0xeb3ecdd0, 0x325306af, 0xd16f567f)
, Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__
mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Modeli
ngToolkit.var"#_RGF_ModTag", (0xc8a21f76, 0xd50266a8, 0x36ae5075, 0x4ece6d0
a, 0x4e546efd), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Not
hing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothin
g, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.NonlinearSystem},
Nothing, ModelingToolkit.NonlinearSystem, Vector{Float64}, Nothing}, Base.P
airs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, Nothing, Nothing}, typeof(Mo
delingToolkit.update_initializeprob!), ComposedFunction{ComposedFunction{ty
peof(identity), typeof(ModelingToolkit.safe_float)}, SymbolicIndexingInterf
ace.TimeIndependentObservedFunction{ModelingToolkit.GeneratedFunctionWrappe
r{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_
arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingTo
olkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x5560ce01, 0x991a4cdf, 0
x392020a7), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:
ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTa
g", ModelingToolkit.var"#_RGF_ModTag", (0x2b19e578, 0x47f62e68, 0x3f23a85d,
0xb87b692a, 0xb5777171), Nothing}}}}, ModelingToolkit.var"#initprobpmap_sp
lit#810"{ModelingToolkit.var"#_getter#806"{Tuple{Returns{StaticArraysCore.S
izedVector{0, Float64, Vector{Float64}}}, ComposedFunction{ModelingToolkit.
PConstructorApplicator{typeof(identity)}, ModelingToolkit.ObservedWrapper{f
alse, ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGenerat
edFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___),
ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x38
3e1f76, 0x30e3ca66, 0xe27ee296, 0x7de466bf, 0xddedf6e9), Nothing}, RuntimeG
eneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkpa
rameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_
ModTag", (0xdef1fe73, 0x41a6768b, 0x43614868, 0x9db8eb5f, 0xb69f9719), Noth
ing}}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}}, ModelingT
oolkit.InitializationMetadata{ModelingToolkit.ReconstructInitializeprob{Mod
elingToolkit.var"#_getter#806"{Tuple{ComposedFunction{ModelingToolkit.PCons
tructorApplicator{typeof(identity)}, ModelingToolkit.ObservedWrapper{true,
ModelingToolkit.GeneratedFunctionWrapper{(2, 3, true), RuntimeGeneratedFunc
tions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), Mo
delingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x7e79
da91, 0xd20b440a, 0x8f31de5e, 0xb3bf1671, 0x1e4c890d), Nothing}, RuntimeGen
eratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkpara
meters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RG
F_ModTag", (0xdc0e8bfb, 0xe657b82a, 0x2b04a79c, 0xdd2049fc, 0x2f912348), No
thing}}}}, Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}
}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}, ComposedFunctio
n{typeof(identity), SymbolicIndexingInterface.TimeDependentObservedFunction
{SymbolicIndexingInterface.ContinuousTimeseries, ModelingToolkit.GeneratedF
unctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunc
tion{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_Mo
dTag", ModelingToolkit.var"#_RGF_ModTag", (0xe2dbe4c4, 0x8637425f, 0xf9877c
30, 0xc6a732b9, 0xb3aed46a), Nothing}, RuntimeGeneratedFunctions.RuntimeGen
eratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingTo
olkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc0ff0587, 0x
8943b463, 0x759a7721, 0x55ab8be5, 0xe5da0c74), Nothing}}, true}}}, Modeling
Toolkit.GetUpdatedU0{SymbolicIndexingInterface.TimeIndependentObservedFunct
ion{ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGenerated
Functions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), Mo
delingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x402c
48b5, 0xfa2314b8, 0x4a877dea, 0xd8553b68, 0xe8202d4a), Nothing}, RuntimeGen
eratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkpara
meters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_Mo
dTag", (0xefb5629c, 0x6f14cbd6, 0xfff3a505, 0x6fdc0cc0, 0x6dc034e6), Nothin
g}}}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingIn
terface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameter
Index{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}}, No
thing}}, ModelingToolkit.SetInitialUnknowns{SymbolicIndexingInterface.Multi
pleSetters{Vector{SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIn
dexingInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStruc
tures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}}}}}, Val{true}}
(SciMLBase.NonlinearLeastSquaresProblem{Vector{Float64}, true, ModelingTool
kit.MTKParameters{Vector{Float64}, StaticArraysCore.SizedVector{0, Float64,
Vector{Float64}}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, SciMLBase.Nonlinear
Function{true, SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionW
rapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:_
_mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Model
ingToolkit.var"#_RGF_ModTag", (0x855d74ab, 0xd2df28ae, 0xeb3ecdd0, 0x325306
af, 0xd16f567f), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFuncti
on{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_
ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc8a21f76, 0xd50266a8, 0x36ae
5075, 0x4ece6d0a, 0x4e546efd), Nothing}}, LinearAlgebra.UniformScaling{Bool
}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing,
Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.Non
linearSystem}, Nothing, ModelingToolkit.NonlinearSystem, Vector{Float64}, N
othing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, Nothing, Noth
ing}(SciMLBase.NonlinearFunction{true, SciMLBase.FullSpecialize, ModelingTo
olkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.Runt
imeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.
var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x855d74ab, 0xd2df28
ae, 0xeb3ecdd0, 0x325306af, 0xd16f567f), Nothing}, RuntimeGeneratedFunction
s.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), Mo
delingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc8a2
1f76, 0xd50266a8, 0x36ae5075, 0x4ece6d0a, 0x4e546efd), Nothing}}, LinearAlg
ebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Not
hing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionC
ache{ModelingToolkit.NonlinearSystem}, Nothing, ModelingToolkit.NonlinearSy
stem, Vector{Float64}, Nothing}(ModelingToolkit.GeneratedFunctionWrapper{(2
, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_
1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolki
t.var"#_RGF_ModTag", (0x855d74ab, 0xd2df28ae, 0xeb3ecdd0, 0x325306af, 0xd16
f567f), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋ou
t, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag",
ModelingToolkit.var"#_RGF_ModTag", (0xc8a21f76, 0xd50266a8, 0x36ae5075, 0x4
ece6d0a, 0x4e546efd), Nothing}}(RuntimeGeneratedFunctions.RuntimeGeneratedF
unction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_Mod
Tag", ModelingToolkit.var"#_RGF_ModTag", (0x855d74ab, 0xd2df28ae, 0xeb3ecdd
0, 0x325306af, 0xd16f567f), Nothing}(nothing), RuntimeGeneratedFunctions.Ru
ntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), Modeli
ngToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc8a21f76
, 0xd50266a8, 0x36ae5075, 0x4ece6d0a, 0x4e546efd), Nothing}(nothing)), Line
arAlgebra.UniformScaling{Bool}(true), nothing, nothing, nothing, nothing, n
othing, nothing, nothing, nothing, nothing, nothing, ModelingToolkit.Observ
edFunctionCache{ModelingToolkit.NonlinearSystem}(Model sys:
Equations (10):
10 standard: see equations(sys)
Unknowns (1): see unknowns(sys)
vφ2ˍt(t) [defaults to -74.9958]
Parameters (45): see parameters(sys)
t
Initial(vφ1ˍt(t)) [defaults to false]
Initial(vφ1ˍtt(t)) [defaults to false]
Initial(vq₄ˍt(t)) [defaults to false]
⋮
Observed (26): see observed(sys), Dict{Any, Any}(SymbolicUtils.BasicSymboli
c{Real}[vq₄(t), q₄(t), vq₂(t), vq₁(t), vq₃(t), q₁(t), q₂(t), q₃(t), φ2ˍt(t)
, vq₄ˍt(t), φ2(t), λ₁(t), φ2ˍtt(t)] => ModelingToolkit.GeneratedFunctionWra
pper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__m
tk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Modelin
gToolkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x5560ce01, 0x991a4cdf
, 0x392020a7), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction
{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_Mo
dTag", ModelingToolkit.var"#_RGF_ModTag", (0x2b19e578, 0x47f62e68, 0x3f23a8
5d, 0xb87b692a, 0xb5777171), Nothing}}(RuntimeGeneratedFunctions.RuntimeGen
eratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_
RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x
5560ce01, 0x991a4cdf, 0x392020a7), Nothing}(nothing), RuntimeGeneratedFunct
ions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___),
ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x2
b19e578, 0x47f62e68, 0x3f23a85d, 0xb87b692a, 0xb5777171), Nothing}(nothing)
), Any[vq₄ˍt(t), φ2ˍtt(t), φ2ˍt(t)] => ModelingToolkit.GeneratedFunctionWra
pper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__m
tk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Modelin
gToolkit.var"#_RGF_ModTag", (0x59806009, 0x122eca51, 0xd6164a75, 0x9414c9c0
, 0xe211bcbc), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction
{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_Mo
dTag", ModelingToolkit.var"#_RGF_ModTag", (0x44b04ca3, 0xf8eac98b, 0x8198dd
8b, 0xa7a5108c, 0x9f72ce11), Nothing}}(RuntimeGeneratedFunctions.RuntimeGen
eratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_
RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x59806009, 0x122eca51, 0x
d6164a75, 0x9414c9c0, 0xe211bcbc), Nothing}(nothing), RuntimeGeneratedFunct
ions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___),
ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x4
4b04ca3, 0xf8eac98b, 0x8198dd8b, 0xa7a5108c, 0x9f72ce11), Nothing}(nothing)
)), false, false, ModelingToolkit, false, true), nothing, Model sys:
Equations (10):
10 standard: see equations(sys)
Unknowns (1): see unknowns(sys)
vφ2ˍt(t) [defaults to -74.9958]
Parameters (45): see parameters(sys)
t
Initial(vφ1ˍt(t)) [defaults to false]
Initial(vφ1ˍtt(t)) [defaults to false]
Initial(vq₄ˍt(t)) [defaults to false]
⋮
Observed (26): see observed(sys), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0], nothing), [0.0], ModelingToolkit.MTKParameters{Vector{Float64},
StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}, Tuple{}, Tuple{}
, Tuple{}, Tuple{}}([0.0, 0.0, 0.0, 0.0, -2.68938672e-6, 382.45895095266985
, 0.0, 1.69327969e-5, 150.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.033398
63e-5, 0.0, 0.0, 0.0], Float64[], (), (), (), ()), nothing, nothing, Base.P
airs{Symbol, Union{}, Tuple{}, @NamedTuple{}}()), ModelingToolkit.update_in
itializeprob!, identity ∘ ModelingToolkit.safe_float ∘ SymbolicIndexingInte
rface.TimeIndependentObservedFunction{ModelingToolkit.GeneratedFunctionWrap
per{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mt
k_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Modeling
Toolkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x5560ce01, 0x991a4cdf,
0x392020a7), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{
(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_Mod
Tag", ModelingToolkit.var"#_RGF_ModTag", (0x2b19e578, 0x47f62e68, 0x3f23a85
d, 0xb87b692a, 0xb5777171), Nothing}}}(ModelingToolkit.GeneratedFunctionWra
pper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__m
tk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Modelin
gToolkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x5560ce01, 0x991a4cdf
, 0x392020a7), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction
{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_Mo
dTag", ModelingToolkit.var"#_RGF_ModTag", (0x2b19e578, 0x47f62e68, 0x3f23a8
5d, 0xb87b692a, 0xb5777171), Nothing}}(RuntimeGeneratedFunctions.RuntimeGen
eratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_
RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x336b2cdb, 0x5c3e3d71, 0x
5560ce01, 0x991a4cdf, 0x392020a7), Nothing}(nothing), RuntimeGeneratedFunct
ions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___),
ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x2
b19e578, 0x47f62e68, 0x3f23a85d, 0xb87b692a, 0xb5777171), Nothing}(nothing)
)), ModelingToolkit.var"#initprobpmap_split#810"{ModelingToolkit.var"#_gett
er#806"{Tuple{Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float
64}}}, ComposedFunction{ModelingToolkit.PConstructorApplicator{typeof(ident
ity)}, ModelingToolkit.ObservedWrapper{false, ModelingToolkit.GeneratedFunc
tionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunctio
n{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag",
ModelingToolkit.var"#_RGF_ModTag", (0x383e1f76, 0x30e3ca66, 0xe27ee296, 0x7
de466bf, 0xddedf6e9), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedF
unction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#
_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xdef1fe73, 0x41a6768b, 0
x43614868, 0x9db8eb5f, 0xb69f9719), Nothing}}}}, Returns{Tuple{}}, Returns{
Tuple{}}, Returns{Tuple{}}}}}(ModelingToolkit.var"#_getter#806"{Tuple{Retur
ns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}}, ComposedFunc
tion{ModelingToolkit.PConstructorApplicator{typeof(identity)}, ModelingTool
kit.ObservedWrapper{false, ModelingToolkit.GeneratedFunctionWrapper{(2, 2,
true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :_
__mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var
"#_RGF_ModTag", (0x383e1f76, 0x30e3ca66, 0xe27ee296, 0x7de466bf, 0xddedf6e9
), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :_
_mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", Model
ingToolkit.var"#_RGF_ModTag", (0xdef1fe73, 0x41a6768b, 0x43614868, 0x9db8eb
5f, 0xb69f9719), Nothing}}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{T
uple{}}}}((Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}
}}(Float64[]), ModelingToolkit.PConstructorApplicator{typeof(identity)}(ide
ntity) ∘ ModelingToolkit.ObservedWrapper{false, ModelingToolkit.GeneratedFu
nctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunct
ion{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag"
, ModelingToolkit.var"#_RGF_ModTag", (0x383e1f76, 0x30e3ca66, 0xe27ee296, 0
x7de466bf, 0xddedf6e9), Nothing}, RuntimeGeneratedFunctions.RuntimeGenerate
dFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var
"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xdef1fe73, 0x41a6768b,
0x43614868, 0x9db8eb5f, 0xb69f9719), Nothing}}}(ModelingToolkit.GeneratedF
unctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunc
tion{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag
", ModelingToolkit.var"#_RGF_ModTag", (0x383e1f76, 0x30e3ca66, 0xe27ee296,
0x7de466bf, 0xddedf6e9), Nothing}, RuntimeGeneratedFunctions.RuntimeGenerat
edFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.va
r"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xdef1fe73, 0x41a6768b
, 0x43614868, 0x9db8eb5f, 0xb69f9719), Nothing}}(RuntimeGeneratedFunctions.
RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingTool
kit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x383e1f76, 0x30
e3ca66, 0xe27ee296, 0x7de466bf, 0xddedf6e9), Nothing}(nothing), RuntimeGene
ratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparam
eters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_Mod
Tag", (0xdef1fe73, 0x41a6768b, 0x43614868, 0x9db8eb5f, 0xb69f9719), Nothing
}(nothing))), Returns{Tuple{}}(()), Returns{Tuple{}}(()), Returns{Tuple{}}(
())))), ModelingToolkit.InitializationMetadata{ModelingToolkit.ReconstructI
nitializeprob{ModelingToolkit.var"#_getter#806"{Tuple{ComposedFunction{Mode
lingToolkit.PConstructorApplicator{typeof(identity)}, ModelingToolkit.Obser
vedWrapper{true, ModelingToolkit.GeneratedFunctionWrapper{(2, 3, true), Run
timeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparam
eters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF
_ModTag", (0x7e79da91, 0xd20b440a, 0x8f31de5e, 0xb3bf1671, 0x1e4c890d), Not
hing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_a
rg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", Modelin
gToolkit.var"#_RGF_ModTag", (0xdc0e8bfb, 0xe657b82a, 0x2b04a79c, 0xdd2049fc
, 0x2f912348), Nothing}}}}, Returns{StaticArraysCore.SizedVector{0, Float64
, Vector{Float64}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}
, ComposedFunction{typeof(identity), SymbolicIndexingInterface.TimeDependen
tObservedFunction{SymbolicIndexingInterface.ContinuousTimeseries, ModelingT
oolkit.GeneratedFunctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.Run
timeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToo
lkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe2dbe4c4, 0x8
637425f, 0xf9877c30, 0xc6a732b9, 0xb3aed46a), Nothing}, RuntimeGeneratedFun
ctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___
, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag"
, (0xc0ff0587, 0x8943b463, 0x759a7721, 0x55ab8be5, 0xe5da0c74), Nothing}},
true}}}, ModelingToolkit.GetUpdatedU0{SymbolicIndexingInterface.TimeIndepen
dentObservedFunction{ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true),
RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkp
arameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF
_ModTag", (0x402c48b5, 0xfa2314b8, 0x4a877dea, 0xd8553b68, 0xe8202d4a), Not
hing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_a
rg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToo
lkit.var"#_RGF_ModTag", (0xefb5629c, 0x6f14cbd6, 0xfff3a505, 0x6fdc0cc0, 0x
6dc034e6), Nothing}}}, SymbolicIndexingInterface.MultipleParametersGetter{S
ymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInter
face.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initi
als, Int64}}}, Nothing}}, ModelingToolkit.SetInitialUnknowns{SymbolicIndexi
ngInterface.MultipleSetters{Vector{SymbolicIndexingInterface.ParameterHookW
rapper{SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.Paramete
rIndex{SciMLStructures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}
}}}}}(Dict{Any, Any}(vφ2(t) => Initial(vφ2(t)), q₂(t) => Initial(q₂(t)), λ₂
(t) => Initial(λ₂(t)), vq₁(t) => Initial(vq₁(t)), vq₂(t) => Initial(vq₂(t))
, x₃(t) => Initial(x₃(t)), q₁(t) => Initial(q₁(t)), λ₁(t) => Initial(λ₁(t))
, q₃(t) => Initial(q₃(t)), vq₄(t) => Initial(vq₄(t))…), Dict{Any, Any}(Init
ial(vφ1ˍt(t)) => false, Initial(vφ1ˍtt(t)) => false, Initial(vq₄ˍt(t)) => f
alse, Initial(vx₃(t)) => -2.68938672e-6, Initial(λ₂(t)) => 382.458950952669
85, Initial(λ₂ˍt(t)) => false, Initial(q₄(t)) => 1.69327969e-5, Initial(vφ1
(t)) => 150.0, Initial(vx₃ˍt(t)) => false, Initial(x₃ˍtt(t)) => false…), Di
ct{Any, Any}(), Symbolics.Equation[], true, ModelingToolkit.ReconstructInit
ializeprob{ModelingToolkit.var"#_getter#806"{Tuple{ComposedFunction{Modelin
gToolkit.PConstructorApplicator{typeof(identity)}, ModelingToolkit.Observed
Wrapper{true, ModelingToolkit.GeneratedFunctionWrapper{(2, 3, true), Runtim
eGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparamete
rs___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_Mo
dTag", (0x7e79da91, 0xd20b440a, 0x8f31de5e, 0xb3bf1671, 0x1e4c890d), Nothin
g}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_
1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingTo
olkit.var"#_RGF_ModTag", (0xdc0e8bfb, 0xe657b82a, 0x2b04a79c, 0xdd2049fc, 0
x2f912348), Nothing}}}}, Returns{StaticArraysCore.SizedVector{0, Float64, V
ector{Float64}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}, C
omposedFunction{typeof(identity), SymbolicIndexingInterface.TimeDependentOb
servedFunction{SymbolicIndexingInterface.ContinuousTimeseries, ModelingTool
kit.GeneratedFunctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.Runtim
eGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolki
t.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe2dbe4c4, 0x8637
425f, 0xf9877c30, 0xc6a732b9, 0xb3aed46a), Nothing}, RuntimeGeneratedFuncti
ons.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :
t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (
0xc0ff0587, 0x8943b463, 0x759a7721, 0x55ab8be5, 0xe5da0c74), Nothing}}, tru
e}}}(ModelingToolkit.var"#_getter#806"{Tuple{ComposedFunction{ModelingToolk
it.PConstructorApplicator{typeof(identity)}, ModelingToolkit.ObservedWrappe
r{true, ModelingToolkit.GeneratedFunctionWrapper{(2, 3, true), RuntimeGener
atedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___,
:t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag",
(0x7e79da91, 0xd20b440a, 0x8f31de5e, 0xb3bf1671, 0x1e4c890d), Nothing}, Ru
ntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :__
_mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.
var"#_RGF_ModTag", (0xdc0e8bfb, 0xe657b82a, 0x2b04a79c, 0xdd2049fc, 0x2f912
348), Nothing}}}}, Returns{StaticArraysCore.SizedVector{0, Float64, Vector{
Float64}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}((Modelin
gToolkit.PConstructorApplicator{typeof(identity)}(identity) ∘ ModelingToolk
it.ObservedWrapper{true, ModelingToolkit.GeneratedFunctionWrapper{(2, 3, tr
ue), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___
mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.v
ar"#_RGF_ModTag", (0x7e79da91, 0xd20b440a, 0x8f31de5e, 0xb3bf1671, 0x1e4c89
0d), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out,
:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag",
ModelingToolkit.var"#_RGF_ModTag", (0xdc0e8bfb, 0xe657b82a, 0x2b04a79c, 0x
dd2049fc, 0x2f912348), Nothing}}}(ModelingToolkit.GeneratedFunctionWrapper{
(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_ar
g_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", Modeling
Toolkit.var"#_RGF_ModTag", (0x7e79da91, 0xd20b440a, 0x8f31de5e, 0xb3bf1671,
0x1e4c890d), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{
(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF
_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xdc0e8bfb, 0xe657b82a, 0x2b0
4a79c, 0xdd2049fc, 0x2f912348), Nothing}}(RuntimeGeneratedFunctions.Runtime
GeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit
.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x7e79da91, 0xd20b4
40a, 0x8f31de5e, 0xb3bf1671, 0x1e4c890d), Nothing}(nothing), RuntimeGenerat
edFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparamete
rs___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_Mo
dTag", (0xdc0e8bfb, 0xe657b82a, 0x2b04a79c, 0xdd2049fc, 0x2f912348), Nothin
g}(nothing))), Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Floa
t64}}}(Float64[]), Returns{Tuple{}}(()), Returns{Tuple{}}(()), Returns{Tupl
e{}}(()))), identity ∘ SymbolicIndexingInterface.TimeDependentObservedFunct
ion{SymbolicIndexingInterface.ContinuousTimeseries, ModelingToolkit.Generat
edFunctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedF
unction{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF
_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe2dbe4c4, 0x8637425f, 0xf98
77c30, 0xc6a732b9, 0xb3aed46a), Nothing}, RuntimeGeneratedFunctions.Runtime
GeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), Modelin
gToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc0ff0587,
0x8943b463, 0x759a7721, 0x55ab8be5, 0xe5da0c74), Nothing}}, true}(Symbolic
IndexingInterface.ContinuousTimeseries(), ModelingToolkit.GeneratedFunction
Wrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:
__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag",
ModelingToolkit.var"#_RGF_ModTag", (0xe2dbe4c4, 0x8637425f, 0xf9877c30, 0xc
6a732b9, 0xb3aed46a), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedF
unction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.v
ar"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc0ff0587, 0x8943b46
3, 0x759a7721, 0x55ab8be5, 0xe5da0c74), Nothing}}(RuntimeGeneratedFunctions
.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), Modelin
gToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe2dbe4c4,
0x8637425f, 0xf9877c30, 0xc6a732b9, 0xb3aed46a), Nothing}(nothing), Runtim
eGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtk
parameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"
#_RGF_ModTag", (0xc0ff0587, 0x8943b463, 0x759a7721, 0x55ab8be5, 0xe5da0c74)
, Nothing}(nothing)))), ModelingToolkit.GetUpdatedU0{SymbolicIndexingInterf
ace.TimeIndependentObservedFunction{ModelingToolkit.GeneratedFunctionWrappe
r{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_
arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingTo
olkit.var"#_RGF_ModTag", (0x402c48b5, 0xfa2314b8, 0x4a877dea, 0xd8553b68, 0
xe8202d4a), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:
ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTa
g", ModelingToolkit.var"#_RGF_ModTag", (0xefb5629c, 0x6f14cbd6, 0xfff3a505,
0x6fdc0cc0, 0x6dc034e6), Nothing}}}, SymbolicIndexingInterface.MultiplePar
ametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{Symbol
icIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLS
tructures.Initials, Int64}}}, Nothing}}(Bool[0, 0, 0, 0, 0, 0, 0, 0, 1, 1,
0, 0, 1], SymbolicIndexingInterface.TimeIndependentObservedFunction{Modelin
gToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.R
untimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolk
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RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingTool
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uple{SciMLBase.TimeGradientWrapper{true, SciMLBase.ODEFunction{true, SciMLB
ase.FullSpecialize, typeof(Main.var"##WeaveSandBox#225".slider_crank_mm!),
Matrix{Float64}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Noth
ing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_
OBSERVED), Nothing, Nothing, Nothing, Nothing}, Vector{Float64}, SciMLBase.
NullParameters}, Vector{Float64}, ADTypes.AutoForwardDiff{nothing, ForwardD
iff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}}, Float64, Tuple{}}}(), 0.0,
ForwardDiff.DerivativeConfig{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag,
Float64}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffE
qTag, Float64}, Float64, 1}}}(ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.O
rdinaryDiffEqTag, Float64}, Float64, 1}[Dual{ForwardDiff.Tag{DiffEqBase.Ord
inaryDiffEqTag, Float64}}(150.0,0.0), Dual{ForwardDiff.Tag{DiffEqBase.Ordin
aryDiffEqTag, Float64}}(60.23881854735783,0.0), Dual{ForwardDiff.Tag{DiffEq
Base.OrdinaryDiffEqTag, Float64}}(-8.758000839578706,0.0), Dual{ForwardDiff
.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}}(-0.03011595948178246,0.0), Dua
l{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}}(-0.00549970328584
6862,0.0), Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}}(0.0
004987093705251409,0.0), Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag,
Float64}}(0.001116832441838903,0.0), Dual{ForwardDiff.Tag{DiffEqBase.Ordin
aryDiffEqTag, Float64}}(22.563680794381472,0.0), Dual{ForwardDiff.Tag{DiffE
qBase.OrdinaryDiffEqTag, Float64}}(29.927249340064723,0.0), Dual{ForwardDif
f.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}}(163.8151483533587,0.0), Dual{
ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}}(96.2495033600122,0.
0), Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}}(-46.827145
22677127,0.0), Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}}
(-1.3149194124530368,0.0), Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTa
g, Float64}}(0.09513052663032795,0.0), Dual{ForwardDiff.Tag{DiffEqBase.Ordi
naryDiffEqTag, Float64}}(5.766166624038283e-14,0.0), Dual{ForwardDiff.Tag{D
iffEqBase.OrdinaryDiffEqTag, Float64}}(-2.155827599770177e-15,0.0), Dual{Fo
rwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}}(0.0,0.0)]), ()), Diff
erentiationInterfaceForwardDiffExt.ForwardDiffTwoArgDerivativePrep{Tuple{Sc
iMLBase.TimeGradientWrapper{true, SciMLBase.ODEFunction{true, SciMLBase.Ful
lSpecialize, typeof(Main.var"##WeaveSandBox#225".slider_crank_mm!), Matrix{
Float64}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, No
thing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVE
D), Nothing, Nothing, Nothing, Nothing}, Vector{Float64}, SciMLBase.NullPar
ameters}, Vector{Float64}, ADTypes.AutoForwardDiff{nothing, ForwardDiff.Tag
{DiffEqBase.OrdinaryDiffEqTag, Float64}}, Float64, Tuple{}}, Float64, Forwa
rdDiff.DerivativeConfig{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float
64}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag,
Float64}, Float64, 1}}}, Tuple{}}(Val{Tuple{SciMLBase.TimeGradientWrapper{t
rue, SciMLBase.ODEFunction{true, SciMLBase.FullSpecialize, typeof(Main.var"
##WeaveSandBox#225".slider_crank_mm!), Matrix{Float64}, Nothing, Nothing, N
othing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Noth
ing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing
, Nothing}, Vector{Float64}, SciMLBase.NullParameters}, Vector{Float64}, AD
Types.AutoForwardDiff{nothing, ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag
, Float64}}, Float64, Tuple{}}}(), 0.0, ForwardDiff.DerivativeConfig{Forwar
dDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Vector{ForwardDiff.Dual{F
orwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}}(Forwar
dDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64,
1}[Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}}(150.0,0.0)
, Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}}(60.238818547
35783,0.0), Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}}(-8
.758000839578706,0.0), Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, F
loat64}}(-0.03011595948178246,0.0), Dual{ForwardDiff.Tag{DiffEqBase.Ordinar
yDiffEqTag, Float64}}(-0.005499703285846862,0.0), Dual{ForwardDiff.Tag{Diff
EqBase.OrdinaryDiffEqTag, Float64}}(0.0004987093705251409,0.0), Dual{Forwar
dDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}}(0.001116832441838903,0.0)
, Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}}(22.563680794
381472,0.0), Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}}(2
9.927249340064723,0.0), Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag,
Float64}}(163.8151483533587,0.0), Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryD
iffEqTag, Float64}}(96.2495033600122,0.0), Dual{ForwardDiff.Tag{DiffEqBase.
OrdinaryDiffEqTag, Float64}}(-46.82714522677127,0.0), Dual{ForwardDiff.Tag{
DiffEqBase.OrdinaryDiffEqTag, Float64}}(-1.3149194124530368,0.0), Dual{Forw
ardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}}(0.09513052663032795,0.0
), Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}}(5.766166624
038283e-14,0.0), Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64
}}(-2.155827599770177e-15,0.0), Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDif
fEqTag, Float64}}(0.0,0.0)]), ())), 1.0e-6, OrdinaryDiffEqRosenbrock.Rodas5
P{0, ADTypes.AutoForwardDiff{nothing, ForwardDiff.Tag{DiffEqBase.OrdinaryDi
ffEqTag, Float64}}, Nothing, typeof(OrdinaryDiffEqCore.DEFAULT_PRECS), Val{
:forward}(), true, nothing, typeof(OrdinaryDiffEqCore.trivial_limiter!), ty
peof(OrdinaryDiffEqCore.trivial_limiter!)}(nothing, OrdinaryDiffEqCore.DEFA
ULT_PRECS, OrdinaryDiffEqCore.trivial_limiter!, OrdinaryDiffEqCore.trivial_
limiter!, ADTypes.AutoForwardDiff(tag=ForwardDiff.Tag{DiffEqBase.OrdinaryDi
ffEqTag, Float64}())), OrdinaryDiffEqCore.trivial_limiter!, OrdinaryDiffEqC
ore.trivial_limiter!, 3), OrdinaryDiffEqCore.DifferentialVarsUndefined(), f
alse), true, 0, SciMLBase.DEStats(124293, 0, 11345, 90760, 11177, 0, 0, 0,
0, 0, 11177, 168, 0.0), nothing, SciMLBase.ReturnCode.Success, nothing, not
hing, nothing)High Tolerances
abstols = 1.0 ./ 10.0 .^ (4:7)
reltols = 1.0 ./ 10.0 .^ (1:4)
setups = [
Dict(:prob_choice => 1, :alg => IDA()),
Dict(:prob_choice => 2, :alg => Rodas5P()),
Dict(:prob_choice => 2, :alg => Rodas4P()),
Dict(:prob_choice => 3, :alg => Rodas5P()),
Dict(:prob_choice => 3, :alg => Rodas4P()),
Dict(:prob_choice => 3, :alg => FBDF()),
]
labels = ["IDA (DAE)" "Rodas5P (MTK)" "Rodas4P (MTK)" "Rodas5P (MM)" "Rodas4P (MM)" "FBDF (MM)"]
wp = WorkPrecisionSet(probs, abstols, reltols, setups;
names = labels, appxsol = refs, save_everystep = false,
maxiters = Int(1e6), numruns = 5)
plot(wp, title = "Slider-Crank: All Formulations (High Tol)")
Medium Tolerances
abstols = 1.0 ./ 10.0 .^ (5:7)
reltols = 1.0 ./ 10.0 .^ (2:4)
setups = [
Dict(:prob_choice => 1, :alg => IDA()),
Dict(:prob_choice => 2, :alg => Rodas5P()),
Dict(:prob_choice => 2, :alg => Rodas4P()),
Dict(:prob_choice => 3, :alg => Rodas5P()),
Dict(:prob_choice => 3, :alg => Rodas4P()),
]
labels = ["IDA (DAE)" "Rodas5P (MTK)" "Rodas4P (MTK)" "Rodas5P (MM)" "Rodas4P (MM)"]
wp = WorkPrecisionSet(probs, abstols, reltols, setups;
names = labels, appxsol = refs, save_everystep = false,
maxiters = Int(1e6), numruns = 5)
plot(wp, title = "Slider-Crank: All Formulations (Medium Tol)")
Timeseries Errors (L2)
abstols = 1.0 ./ 10.0 .^ (4:7)
reltols = 1.0 ./ 10.0 .^ (1:4)
setups = [
Dict(:prob_choice => 2, :alg => Rodas5P()),
Dict(:prob_choice => 2, :alg => Rodas4P()),
Dict(:prob_choice => 3, :alg => Rodas5P()),
Dict(:prob_choice => 3, :alg => Rodas4P()),
]
labels = ["Rodas5P (MTK)" "Rodas4P (MTK)" "Rodas5P (MM)" "Rodas4P (MM)"]
wp = WorkPrecisionSet(probs, abstols, reltols, setups;
names = labels, appxsol = refs, save_everystep = false,
maxiters = Int(1e6), numruns = 5, error_estimate = :l2)
plot(wp, title = "Slider-Crank: Timeseries Error (L2)")
Verification against ARCHIMEDE Reference
The IVP Test Set (crank.f, solut subroutine) provides reference values at t = 0.1. We verify our solution reproduces these values.
archimede_refs = Dict(
"φ₂" => -0.331173498825626,
"x₃" => 0.169737332842786,
"q₁" => 0.1893192899613509e-3,
"q₂" => 0.2375751249879174e-4,
"q₃" => -0.5323896770569702e-5,
"q₄" => -0.8363313279112129e-5,
"λ₁" => -62.32935833287916,
"λ₂" => -163.7920993367306,
"λ₃" => 25.29857947066878,
)
# Mass-matrix form indices: [p(1:7), v(8:14), λ(15:17)]
idxmap = [("φ₂", 2), ("x₃", 3), ("q₁", 4), ("q₂", 5), ("q₃", 6), ("q₄", 7),
("λ₁", 15), ("λ₂", 16), ("λ₃", 17)]
sol_final = ref_sol.u[end]
println("=== Verification at t = 0.1 ===")
println("Variable | ARCHIMEDE Reference | Our Solution | Rel Error")
println("-"^75)
for (name, idx) in idxmap
ref_val = archimede_refs[name]
our_val = sol_final[idx]
relerr = abs(ref_val) > 0 ? abs((our_val - ref_val) / ref_val) : abs(our_val)
status = relerr < 1e-3 ? "✓" : (relerr < 1e-1 ? "~" : "✗")
println("$(rpad(name, 12))| $(lpad(string(ref_val), 21)) | $(lpad(string(round(our_val, sigdigits=10)), 21)) | $(relerr) $status")
end
# Overlay ARCHIMEDE reference point on q₁ timeseries
p_verify = plot(ref_sol, idxs = [4], title = "Verification: Elastic Mode q₁",
xlabel = "Time (s)", ylabel = "Amplitude", lw = 2, label = "SciML Rodas5P")
scatter!(p_verify, [0.1], [0.1893192899613509e-3],
label = "ARCHIMEDE Reference", color = :red, markersize = 8)
plot(p_verify)=== Verification at t = 0.1 ===
Variable | ARCHIMEDE Reference | Our Solution | Rel Error
---------------------------------------------------------------------------
φ₂ | -0.331173498825626 | -0.3311735023 | 1.05661652126
33346e-8 ✓
x₃ | 0.169737332842786 | 0.1697373296 | 1.90141116248
40277e-8 ✓
q₁ | 0.0001893192899613509 | 0.000189242689 | 0.00040461280
04282341 ✓
q₂ | 2.375751249879174e-5 | 2.375891525e-5 | 5.90444468590
6018e-5 ✓
q₃ | -5.323896770569702e-6 | -5.327102156e-6 | 0.00060207509
33957827 ✓
q₄ | -8.363313279112129e-6 | -8.366365694e-6 | 0.00036497670
660000765 ✓
λ₁ | -62.32935833287916 | -62.33911336 | 0.00015650768
640384412 ✓
λ₂ | -163.7920993367306 | -163.7681916 | 0.00014596394
888443659 ✓
λ₃ | 25.29857947066878 | -18.21047117 | 1.71982188540
59253 ✗
Appendix
These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: https://github.com/SciML/SciMLBenchmarks.jl. For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization https://sciml.ai.
To locally run this benchmark, do the following commands:
using SciMLBenchmarks
SciMLBenchmarks.weave_file("benchmarks/DAE","slider_crank.jmd")Computer Information:
Julia Version 1.10.11
Commit a2b11907d7b (2026-03-09 14:59 UTC)
Build Info:
Official https://julialang.org/ release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 128 × AMD EPYC 7502 32-Core Processor
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
Threads: 1 default, 0 interactive, 1 GC (on 128 virtual cores)
Environment:
JULIA_CPU_THREADS = 128
JULIA_DEPOT_PATH = /cache/julia-buildkite-plugin/depots/5b300254-1738-4989-ae0a-f4d2d937f953:
Package Information:
Status `/cache/build/exclusive-amdci3-0/julialang/scimlbenchmarks-dot-jl/benchmarks/DAE/Project.toml`
[165a45c3] DASKR v2.9.1
[e993076c] DASSL v2.8.0
[f3b72e0c] DiffEqDevTools v2.49.0
⌅ [961ee093] ModelingToolkit v9.84.0
[09606e27] ODEInterfaceDiffEq v3.16.0
⌃ [1dea7af3] OrdinaryDiffEq v6.107.0
[91a5bcdd] Plots v1.41.6
[31c91b34] SciMLBenchmarks v0.1.3
[90137ffa] StaticArrays v1.9.18
⌅ [c3572dad] Sundials v4.28.0
[10745b16] Statistics v1.10.0
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated`And the full manifest:
Status `/cache/build/exclusive-amdci3-0/julialang/scimlbenchmarks-dot-jl/benchmarks/DAE/Manifest.toml`
[47edcb42] ADTypes v1.21.0
[1520ce14] AbstractTrees v0.4.5
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[d1d4a3ce] BitFlags v0.1.9
[62783981] BitTwiddlingConvenienceFunctions v0.1.6
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⌃ [7c1d4256] DynamicPolynomials v0.6.3
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[28b8d3ca] GR v0.73.24
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⌃ [86223c79] Graphs v1.13.1
[42e2da0e] Grisu v1.0.2
[cd3eb016] HTTP v1.11.0
⌅ [eafb193a] Highlights v0.5.3
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⌅ [682c06a0] JSON v0.21.4
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⌃ [becaefa8] OrdinaryDiffEqExtrapolation v1.13.0
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[1344f307] OrdinaryDiffEqLowOrderRK v1.10.0
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⌃ [2d112036] OrdinaryDiffEqSDIRK v1.11.0
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⌃ [e3e12d00] OrdinaryDiffEqStabilizedIRK v1.10.0
[358294b1] OrdinaryDiffEqStabilizedRK v1.8.0
[fa646aed] OrdinaryDiffEqSymplecticRK v1.11.0
[b1df2697] OrdinaryDiffEqTsit5 v1.9.0
[79d7bb75] OrdinaryDiffEqVerner v1.11.0
[90014a1f] PDMats v0.11.37
[69de0a69] Parsers v2.8.3
[ccf2f8ad] PlotThemes v3.3.0
[995b91a9] PlotUtils v1.4.4
[91a5bcdd] Plots v1.41.6
[e409e4f3] PoissonRandom v0.4.7
[f517fe37] Polyester v0.7.19
[1d0040c9] PolyesterWeave v0.2.2
⌃ [d236fae5] PreallocationTools v0.4.34
⌅ [aea7be01] PrecompileTools v1.2.1
[21216c6a] Preferences v1.5.2
[27ebfcd6] Primes v0.5.7
[43287f4e] PtrArrays v1.4.0
[1fd47b50] QuadGK v2.11.2
[3cdcf5f2] RecipesBase v1.3.4
[01d81517] RecipesPipeline v0.6.12
[731186ca] RecursiveArrayTools v3.48.0
[189a3867] Reexport v1.2.2
[05181044] RelocatableFolders v1.0.1
[ae029012] Requires v1.3.1
[ae5879a3] ResettableStacks v1.2.0
[79098fc4] Rmath v0.9.0
[47965b36] RootedTrees v2.25.0
[7e49a35a] RuntimeGeneratedFunctions v0.5.17
[9dfe8606] SCCNonlinearSolve v1.11.0
[94e857df] SIMDTypes v0.1.0
[0bca4576] SciMLBase v2.149.0
[31c91b34] SciMLBenchmarks v0.1.3
[19f34311] SciMLJacobianOperators v0.1.12
[a6db7da4] SciMLLogging v1.9.1
[c0aeaf25] SciMLOperators v1.15.1
[431bcebd] SciMLPublic v1.0.1
[53ae85a6] SciMLStructures v1.10.0
[6c6a2e73] Scratch v1.3.0
[efcf1570] Setfield v1.1.2
[992d4aef] Showoff v1.0.3
[777ac1f9] SimpleBufferStream v1.2.0
[727e6d20] SimpleNonlinearSolve v2.11.0
[699a6c99] SimpleTraits v0.9.5
[a2af1166] SortingAlgorithms v1.2.2
[0a514795] SparseMatrixColorings v0.4.24
[276daf66] SpecialFunctions v2.7.1
[860ef19b] StableRNGs v1.0.4
[aedffcd0] Static v1.3.1
[0d7ed370] StaticArrayInterface v1.9.0
[90137ffa] StaticArrays v1.9.18
[1e83bf80] StaticArraysCore v1.4.4
[82ae8749] StatsAPI v1.8.0
[2913bbd2] StatsBase v0.34.10
[4c63d2b9] StatsFuns v1.5.2
[7792a7ef] StrideArraysCore v0.5.8
[69024149] StringEncodings v0.3.7
[09ab397b] StructArrays v0.7.2
⌅ [c3572dad] Sundials v4.28.0
[2efcf032] SymbolicIndexingInterface v0.3.46
⌅ [19f23fe9] SymbolicLimits v0.2.3
⌅ [d1185830] SymbolicUtils v3.32.0
⌅ [0c5d862f] Symbolics v6.58.0
[3783bdb8] TableTraits v1.0.1
[bd369af6] Tables v1.12.1
[ed4db957] TaskLocalValues v0.1.3
[62fd8b95] TensorCore v0.1.1
[8ea1fca8] TermInterface v2.0.0
[1c621080] TestItems v1.0.0
[8290d209] ThreadingUtilities v0.5.5
[a759f4b9] TimerOutputs v0.5.29
[3bb67fe8] TranscodingStreams v0.11.3
[410a4b4d] Tricks v0.1.13
[781d530d] TruncatedStacktraces v1.4.0
[5c2747f8] URIs v1.6.1
[3a884ed6] UnPack v1.0.2
[1cfade01] UnicodeFun v0.4.1
[1986cc42] Unitful v1.28.0
[a7c27f48] Unityper v0.1.6
[41fe7b60] Unzip v0.2.0
[81def892] VersionParsing v1.3.0
[44d3d7a6] Weave v0.10.12
[ddb6d928] YAML v0.4.16
[c2297ded] ZMQ v1.5.1
[6e34b625] Bzip2_jll v1.0.9+0
[83423d85] Cairo_jll v1.18.5+1
[655fdf9c] DASKR_jll v1.0.1+0
[ee1fde0b] Dbus_jll v1.16.2+0
[2702e6a9] EpollShim_jll v0.0.20230411+1
[2e619515] Expat_jll v2.7.3+0
[b22a6f82] FFMPEG_jll v8.0.1+0
[a3f928ae] Fontconfig_jll v2.17.1+0
[d7e528f0] FreeType2_jll v2.13.4+0
[559328eb] FriBidi_jll v1.0.17+0
[0656b61e] GLFW_jll v3.4.1+0
[d2c73de3] GR_jll v0.73.24+0
[b0724c58] GettextRuntime_jll v0.22.4+0
[61579ee1] Ghostscript_jll v9.55.1+0
[020c3dae] Git_LFS_jll v3.7.0+0
[f8c6e375] Git_jll v2.53.0+0
[7746bdde] Glib_jll v2.86.3+0
[3b182d85] Graphite2_jll v1.3.15+0
[2e76f6c2] HarfBuzz_jll v8.5.1+0
[1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
[aacddb02] JpegTurbo_jll v3.1.4+0
[c1c5ebd0] LAME_jll v3.100.3+0
[88015f11] LERC_jll v4.0.1+0
[1d63c593] LLVMOpenMP_jll v18.1.8+0
[dd4b983a] LZO_jll v2.10.3+0
⌅ [e9f186c6] Libffi_jll v3.4.7+0
[7e76a0d4] Libglvnd_jll v1.7.1+1
[94ce4f54] Libiconv_jll v1.18.0+0
[4b2f31a3] Libmount_jll v2.41.3+0
[89763e89] Libtiff_jll v4.7.2+0
[38a345b3] Libuuid_jll v2.41.3+0
[856f044c] MKL_jll v2025.2.0+0
[c771fb93] ODEInterface_jll v0.0.2+0
[e7412a2a] Ogg_jll v1.3.6+0
[9bd350c2] OpenSSH_jll v10.2.1+0
[458c3c95] OpenSSL_jll v3.5.5+0
[efe28fd5] OpenSpecFun_jll v0.5.6+0
[91d4177d] Opus_jll v1.6.1+0
[36c8627f] Pango_jll v1.57.0+0
⌅ [30392449] Pixman_jll v0.44.2+0
[c0090381] Qt6Base_jll v6.10.2+1
[629bc702] Qt6Declarative_jll v6.10.2+1
[ce943373] Qt6ShaderTools_jll v6.10.2+1
[6de9746b] Qt6Svg_jll v6.10.2+0
[e99dba38] Qt6Wayland_jll v6.10.2+1
[f50d1b31] Rmath_jll v0.5.1+0
⌅ [fb77eaff] Sundials_jll v5.2.2+0
[a44049a8] Vulkan_Loader_jll v1.3.243+0
[a2964d1f] Wayland_jll v1.24.0+0
[ffd25f8a] XZ_jll v5.8.2+0
[f67eecfb] Xorg_libICE_jll v1.1.2+0
[c834827a] Xorg_libSM_jll v1.2.6+0
[4f6342f7] Xorg_libX11_jll v1.8.13+0
[0c0b7dd1] Xorg_libXau_jll v1.0.13+0
[935fb764] Xorg_libXcursor_jll v1.2.4+0
[a3789734] Xorg_libXdmcp_jll v1.1.6+0
[1082639a] Xorg_libXext_jll v1.3.8+0
[d091e8ba] Xorg_libXfixes_jll v6.0.2+0
[a51aa0fd] Xorg_libXi_jll v1.8.3+0
[d1454406] Xorg_libXinerama_jll v1.1.7+0
[ec84b674] Xorg_libXrandr_jll v1.5.6+0
[ea2f1a96] Xorg_libXrender_jll v0.9.12+0
[c7cfdc94] Xorg_libxcb_jll v1.17.1+0
[cc61e674] Xorg_libxkbfile_jll v1.2.0+0
[e920d4aa] Xorg_xcb_util_cursor_jll v0.1.6+0
[12413925] Xorg_xcb_util_image_jll v0.4.1+0
[2def613f] Xorg_xcb_util_jll v0.4.1+0
[975044d2] Xorg_xcb_util_keysyms_jll v0.4.1+0
[0d47668e] Xorg_xcb_util_renderutil_jll v0.3.10+0
[c22f9ab0] Xorg_xcb_util_wm_jll v0.4.2+0
[35661453] Xorg_xkbcomp_jll v1.4.7+0
[33bec58e] Xorg_xkeyboard_config_jll v2.44.0+0
[c5fb5394] Xorg_xtrans_jll v1.6.0+0
[8f1865be] ZeroMQ_jll v4.3.6+0
[3161d3a3] Zstd_jll v1.5.7+1
[35ca27e7] eudev_jll v3.2.14+0
[214eeab7] fzf_jll v0.61.1+0
[a4ae2306] libaom_jll v3.13.1+0
[0ac62f75] libass_jll v0.17.4+0
[1183f4f0] libdecor_jll v0.2.2+0
[2db6ffa8] libevdev_jll v1.13.4+0
[f638f0a6] libfdk_aac_jll v2.0.4+0
[36db933b] libinput_jll v1.28.1+0
[b53b4c65] libpng_jll v1.6.55+0
[a9144af2] libsodium_jll v1.0.21+0
[f27f6e37] libvorbis_jll v1.3.8+0
[009596ad] mtdev_jll v1.1.7+0
[1317d2d5] oneTBB_jll v2022.0.0+1
⌅ [1270edf5] x264_jll v10164.0.1+0
[dfaa095f] x265_jll v4.1.0+0
[d8fb68d0] xkbcommon_jll v1.13.0+0
[0dad84c5] ArgTools v1.1.1
[56f22d72] Artifacts
[2a0f44e3] Base64
[ade2ca70] Dates
[8ba89e20] Distributed
[f43a241f] Downloads v1.6.0
[7b1f6079] FileWatching
[9fa8497b] Future
[b77e0a4c] InteractiveUtils
[4af54fe1] LazyArtifacts
[b27032c2] LibCURL v0.6.4
[76f85450] LibGit2
[8f399da3] Libdl
[37e2e46d] LinearAlgebra
[56ddb016] Logging
[d6f4376e] Markdown
[a63ad114] Mmap
[ca575930] NetworkOptions v1.2.0
[44cfe95a] Pkg v1.10.0
[de0858da] Printf
[3fa0cd96] REPL
[9a3f8284] Random
[ea8e919c] SHA v0.7.0
[9e88b42a] Serialization
[1a1011a3] SharedArrays
[6462fe0b] Sockets
[2f01184e] SparseArrays v1.10.0
[10745b16] Statistics v1.10.0
[4607b0f0] SuiteSparse
[fa267f1f] TOML v1.0.3
[a4e569a6] Tar v1.10.0
[8dfed614] Test
[cf7118a7] UUIDs
[4ec0a83e] Unicode
[e66e0078] CompilerSupportLibraries_jll v1.1.1+0
[deac9b47] LibCURL_jll v8.4.0+0
[e37daf67] LibGit2_jll v1.6.4+0
[29816b5a] LibSSH2_jll v1.11.0+1
[c8ffd9c3] MbedTLS_jll v2.28.2+1
[14a3606d] MozillaCACerts_jll v2023.1.10
[4536629a] OpenBLAS_jll v0.3.23+4
[05823500] OpenLibm_jll v0.8.5+0
[efcefdf7] PCRE2_jll v10.42.0+1
[bea87d4a] SuiteSparse_jll v7.2.1+1
[83775a58] Zlib_jll v1.2.13+1
[8e850b90] libblastrampoline_jll v5.11.0+0
[8e850ede] nghttp2_jll v1.52.0+1
[3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`