Improbability of collisions in Newtonian gravitational systems of specified angular momentum
Abstract
The angular momentum integral of the equations of motion of the nbody problem of celestial mechanics defines a family of lower dimensional analytic manifolds in the phase space. It is shown that if n is greater than two, then the intersection of the set of initial conditions which lead to collision with each manifold is of measure zero and of Baire first category in the manifold. Thus, the collision initiating set satisfying an arbitrary value of angular momentum is small in both a measure theoretic and topological sense. It follows as a corollary that the converse of Sundman's theorem of total collapse is not true when n is greater than two.
 Publication:

SIAM Journal of Applied Mathematics
 Pub Date:
 February 1979
 Bibcode:
 1979SJAM...36..123U
 Keywords:

 Angular Momentum;
 Collisions;
 Gravitation Theory;
 Many Body Problem;
 Newton Theory;
 Probability Theory;
 Boundary Value Problems;
 Celestial Mechanics;
 Equations Of Motion;
 Gravitational Collapse;
 Gravitational Effects;
 Manifolds (Mathematics);
 Astronomy