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$\begingroup$ interesting! thanks. Do you have any reference for the discrete least action principal and its variation I can read up on? How would this work for e.g. a constraint function that was for an ellipsoid rather than the sphere? $\endgroup$
– Not a chance
Commented Jun 23 at 15:53
$\begingroup$ Glad it helped. Yes, this generalises to any holonomic constraint. The trick is that the force is along the normal of the surface at position $\vec r_n$ with the leapfrog velocity times surrounding it $v_{n-1/2},v_{n+1/2}$. For the discrete least action, I first read about it in Lie group Integrators by Keenan Crane. $\endgroup$
– LPZ
Commented Jun 23 at 17:11

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