Improbability of collisions in a Newtonian gravitational system 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 or equal to 3, 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, when n is greater than or equal to 3 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 or equal to 3.
 Publication:

Ph.D. Thesis
 Pub Date:
 1975
 Bibcode:
 1975PhDT.........1U
 Keywords:

 Angular Momentum;
 Celestial Mechanics;
 Gravitation Theory;
 Newton Theory;
 Problem Solving;
 Astrodynamics;
 Equations Of Motion;
 Gravitational Collapse;
 Mass Distribution;
 Astrophysics