Approach to theN-Body Problem with Hard-Sphere Interaction Applied to the Collision Domains of Three Bodies

Abstract

We present a simple numerical method for determining the phase-space domains that correspond to a chain of successive collisions among $N$ hard spheres. The method is applied to the three-body problem, and it is shown to yield with ease results that are difficult to obtain analytically. The exact phase-space domains corresponding to the allowed collision chains among three spheres are described in full detail for the coplanar case.