N-body Toy
resium.com
resium.com
Did you encounter the effect I call "lost" momentum that occurs around very close approaches when the time quantum is constant? It manifests by particles seeming to gain kinetic energy over time until they fly away. One way of minimising it is to switch to a more precise and accurate force calculation whenever the distance between two particles becomes less than $\epsilon$.
I find the calculation for small distances to be unpredictable, one easy way to test it is to place two particles with small gravity and a large attractive charge. Occasionally close passes cause explosive motion, while other times it hardly overcomes gravity.