I have the following code:

```
# Falling mass, attached to non-linear spring without compression stiffness,
# initially moving upwards with 4 m/s.
using ModelingToolkit, OrdinaryDiffEq, PyPlot, LinearAlgebra
G_EARTH = Float64[0.0, 0.0, -9.81] # gravitational acceleration [m/s²]
L0 = -10.0 # initial spring length [m]
V0 = 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)
simple_sys = structural_simplify(sys)
duration = 10.0
dt = 0.02
tol = 1e-6
tspan = (0.0, duration)
ts = 0:dt:duration
u0 = zeros(6)
u0[3] = L0
u0[6] = V0
prob = ODEProblem(simple_sys, u0, tspan)
@time sol = solve(prob, Rodas5(), dt=dt, abstol=tol, reltol=tol, saveat=ts)
X = sol.t
POS_Z = sol(X, idxs=pos[3])
VEL_Z = sol(X, idxs=vel[3])
lns1 = plot(X, POS_Z, color="green", label="pos_z")
xlabel("time [s]")
ylabel("pos_z [m]")
lns2 = plot(X, L0.+0.005 .* sol[c_spring], color="grey", label="c_spring")
grid(true)
legend()
twinx()
ylabel("vel_z [m/s]")
lns3 = plot(X, VEL_Z, color="red", label="vel_z")
lns = vcat(lns1, lns2, lns3)
labs = [l.get_label() for l in lns]
legend(lns, labs)
PyPlot.show(block=false)
nothing
```

Output is the following plot:

This is a mass, attached to a non-linear spring-damper element. I was reading that for better accuracy I should reset the integrator when a discontinuity is happening.

How could I do this?

See also: GitHub - ufechner7/Tethers.jl: Tether models

This is material intended for teaching, so if you see anything I could improve please tell me…