What happens in the equations of motion if two point masses collide? They will move past each other in a straight line, and will have only an infinitely smal moment of infinite fource. How to represent that without the singularity? A way to look at this is to parameterize the phase space trajectory in terms of a regularization of the potential energy: 1 / (a + r^2) And then take the limit of that trajectory as a->0. ( Can tricks be used as in infinitesimal analysis? ) Related? http://mathoverflow.net/questions/97391/how-to-deal-with-the-singular-reduction-of-the-hamiltonian-n-body-problem Wait..