Collision Singularities in Celestial Mechanics

Abstract

A general collision singularity of the n-body problem in which several clusters of particles collapse simultaneously is replaced by a collision manifold. The flow of the original problem is extended to the collision manifold. The flow on the collision manifold is studied and used to study the asymptotic behaviour of collision orbits. The work of Saari and Hulkower is generalized and it is shown that near any collision singularity of the n-body problem none of the clusters enters into an infinite spin. In order to do that, the manifold of collinear configurations is studied as an embedded submanifold of the unit sphere.