In this model I try to describe the kinematics of a point moving along a beziercurve b[u] (bezier parameter 0<u<1) with prescribed velocity v[u]. The motion is described by timedependent bezierparameter u[t] and angle of tangent \[Psi] [t ]
beziercurve(examplary):
b = BezierFunction[{{0, 0}, {1, 0}, {1, 1}}]
simulating constant velocity
v=1&
sol = NDSolveValue [{
\[Psi]'[ t ] ==v[u[t]] b''[u[t]] . Cross[b'[u[t]]]/(b'[u[t]] . b'[u[t]])^(3/2),
u'[t] ==v[u[t]] {Cos[\[Psi] [t ]], Sin[\[Psi] [t ]]} . b'[u[t]]/b'[u[t]] . b'[u[t]],
\[Psi][0] == 0, u[0] == 0,WhenEvent[u[t] == 1, "StopIntegration"] }, {\[Psi], u}, {t, 0,3 } ]
T = sol[[1]]["Domain"][[1, -1]]
Plot[Through[sol[t]] // Evaluate, {t, 0, T }, PlotStyle -> {Blue, Red}]
model works fine as expected.
But if I change the velocity starting with v[0]==0
v = Min[1, (#/.1)^2] &
NDSolve won't start anymore and returns u[t]==0 and \[Psi][t]==0!
What's wrong here? Thanks!
Min[1, 0.] == 0.? – Michael E2 Oct 18 '21 at 18:44b[u]? And we know thatBezierCurveis difference fromBezierFunction. https://mathematica.stackexchange.com/a/251536/72111 – cvgmt Oct 19 '21 at 00:49BezierFunction– Ulrich Neumann Oct 19 '21 at 06:02v[u]are necessary to leave the equilibrium ? – Ulrich Neumann Oct 19 '21 at 06:10