Very cool! Game rigid body engines (to my knowledge) usually use symplectic Euler (v^{n+1} = v^n + h M^{-1} F^n, q^{n+1} = q^n + h v^n) with a Moreau/Stewart-Tr

Very cool! Game rigid body engines (to my knowledge) usually use symplectic Euler (v^{n+1} = v^n + h M^{-1} F^n, q^{n+1} = q^n + h v^n) with a Moreau/Stewart-Trinkle velocity level discretization of non-penetration constraint (effectively impulses), usually lobbing off the quadratic velocity term (so no precession). These constraints are typically solved in a (projected) Gauss-Seidel fashion to horribly loose tolerances, with liberal post-stabilization thrown in. Outside of rigid bodies, for the most part in games, these days, you don't get 'simulations' that can be derived from a variational principle, but that are instead constraint satisfaction problems with some notion of momentum hacked in the side (see 'Position Based Dynamics', 'Shape Matching'). The movie folks have larger compute time budgets, and I've seen various geometric integrators used there. I know of at least one studio that uses implicit midpoint for thin shell simulation. The Cal-Tech influence has wormed its way into the graphics research world, at least, and you see some papers pop up there frequently looking at geometric integrators. This Danish guy (I'm forgetting his name) at Disney publishes papers every now and then on the topic.