particle-in-tube-new

[Peter230655]

I hope now I did the branching correctly.

A particle in 3D must move from A to B and must stay in a tube definded by a parametric curve and a radius.
(Essentially like the drone, but I switched to a particle to get simple (=faster) EOMs)

Here one can see the following:
Trying to get the distance from the particle to the curve results in a nonlinear equation for the parameter which gives the point of the curve with smallest distance. I make this an additional rom, and the parameter n additional state variable. to ensure the particle stays inside the tube, I add another eom: dist = distance, and bound dist <= radius of tube.at some intermediate time tm the particle should move through a gate, modelled as a circle with center on the curve. To do this, I introduce yet another state variable and another specified variable, gate_h, and add gate = gate_h * distance. I bound gate_h >= 1 and set the instance constraint gate(tm) = radius of the gate.

Most of this is in other PRs, but I find maybe nicely summarized here.

[Peter230655]

Now it traces the particle in the tube. I think, this shows nicely, how the particle does go through the gate, at the place of the gate closest to the wall of the tube - which makes sense as the energy should be minimized.