I'm trying to develop a physics simulation and I want to implement a fourth-order symplectic integration method. The problem is that I must be getting the math wrong, since my simulation is not working at all when using the symplectic integrator (as compared to a fourth-order Runge-Kutta integrator that works reasonably well for the simulation). I've been googling this forever and all I can find are scientific articles on the subject. I tried to adapt the method used in the articles, but am having no luck. I want to know if anyone has source code for a simulation that makes use of symplectic integrators, preferably to simulate a gravitational field but any symplectic integrator would do. What language the source is in doesn't matter too much, but I would appreciate a language using C-style syntax. Thanks!
As you asked for source code: From HERE you can download MATLAB and FORTRAN code for symplectic methods for Hamiltonian systems and symmetric methods for reversible problems. And a lot of other methods for dealing with diff equations too.
And in THIS paper you can find the description of the algorithms.
Edit
If you use Mathematica this may help too.