Add mwe02.jl

mwes/mwe02.jl

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+# Example two: Falling mass, attached to non-linear spring without compression stiffness,
+# initially moving upwards with 4 m/s, using a callback to precisely calculate the discontinuities
+using ModelingToolkit, OrdinaryDiffEq, LinearAlgebra
+
+G_EARTH  = Float64[0.0, 0.0, -9.81]             # gravitational acceleration [m/s²]
+L0::Float64 = -10.0                             # initial spring length      [m]
+V0::Float64 = 4                                 # initial velocity           [m/s]
+
+# model, Z component upwards
+@parameters mass=1.0 c_spring0=50.0 damping=0.5 l0=L0
+@variables t pos(t)[1:3] = [0.0, 0.0,  L0]
+@variables   vel(t)[1:3] = [0.0, 0.0,  V0] 
+@variables   acc(t)[1:3] = G_EARTH
+@variables unit_vector(t)[1:3]  = [0.0, 0.0, -sign(L0)]
+@variables c_spring(t) = c_spring0
+@variables spring_force(t)[1:3] = [0.0, 0.0, 0.0]
+@variables force(t) = 0.0 norm1(t) = abs(l0) spring_vel(t) = 0.0
+D = Differential(t)
+
+eqs = vcat(D.(pos)      ~ vel,
+           D.(vel)      ~ acc,
+           norm1        ~ norm(pos),
+           unit_vector  ~ -pos/norm1,         # direction from point mass to origin
+           spring_vel   ~ -unit_vector ⋅ vel,
+           c_spring     ~ c_spring0 * (norm1 > abs(l0)),
+           spring_force ~ (c_spring * (norm1 - abs(l0)) + damping * spring_vel) * unit_vector,
+           acc          ~ G_EARTH + spring_force/mass)
+
+@named sys = ODESystem(eqs, t; continuous_events = [norm(pos) ~ abs(L0)])
+simple_sys = structural_simplify(sys)
+
+
+duration = 10.0
+dt = 0.02
+tol = 1e-6
+tspan = (0.0, duration)
+ts    = 0:dt:duration
+# initial state
+u0 = Dict(pos=>[0,0,L0], vel=>[0,0,V0])
+
+# function condition(u, t, integrator) # Event when condition(u,t,integrator) == 0
+#     norm(u[1:3]) - abs(L0)
+# end
+# function affect!(integrator)
+#     println(integrator.t)
+# end
+# cb = ContinuousCallback(condition, affect!)
+
+prob = ODEProblem(simple_sys, u0, tspan)
+sol = solve(prob, Rodas5(), dt=dt, abstol=tol, reltol=tol, saveat=ts)
+nothing