Chin's symplectic 4th order methods

[Thiamin]

Siu A Chin describes some very interesting sounding integration methods with only positive time steps. See here(pdf), or lots more papers here.
Previously I thought I would have to choose between energy preserving(Verlet or variants) or higher order(RK4), but this seems like a way to get the best of both worlds.
They also claim much better accuracy than RK4.
I got interested in it when I heard Algorithm C described as 'the new gold standard' here.

Has anyone here already looked at using something like this in their physics engine ? If so I'd be very interested to hear results and would appreciate any tips on implementation.

I'm interested in it for my live form-finding/analysis CAD plugin Kangaroo, and want something that can be used for a wide range of different types of simulation - So perhaps slightly different requirements than a typical game engine.

[Dirk Gregorius]

I think that geometric integrators are the way to go. It is also questionable whether better accuracy is something that is required for games and movies. Note that the integrators need to be able to deal with constraints which requires solving a DAE rather than an ODE. For a nice introduction with some nice references look here: http://stochastix.wordpress.com/2008/06 ... tegrators/

[Thiamin]

Thanks Dirk, that does indeed look like a nice intro and collection of references.

[ngbinh]

We've been using our simulation on various robotics experiments and get close to experimental accuracy with just semi implicit Euler integrator. You may have problem with linear integrator when dealing with highly articulated bodies with many bodies connected through joints. But for that situation, higher order integrators could only help a little as the right way to deal with it is using reduced coordinate approaches.

Moreover, having higher order integrator works right in physical simulation is not an easy task, it usually requires rewriting the whole formulation as shown in here this paper :F.R. Potra, M. Anitescu, B. Gavrea, and J.C. Trinkle. Linearly implicit trapezoidal method for integrating stiff multibody dynamics with contact, joints, and friction. International Journal for Numerical Methods in Engineering, 66(7):1079-1124, December 2005. ( http://www.cs.rpi.edu/~trink/Papers/PAGTijnme05.pdf ). And the final form is usually non-linear mixed complementarity problem and there is no robust way of solving.

HTH