A Global Regularisation of the Gravitational NBody Problem
Abstract
The work of Aarseth and Zare (1974) is extended to provide aglobal regularisation of the classical gravitational threebody problem: by transformation of the variables in a way that does not depend on the particular configuration, we obtain equations of motion which are regular with respect to collisions between any pair of particles. The only cases excepted are those in which collisions between more than one pair occur simultaneously and those in which at least one of the masses vanishes. However, by means of the same principles the restricted problem is regularised globally if collisions between the two primaries are excluded. Results of numerical tests are summarised, and the theory is generalised to provide global regularisations, first, for perturbed threebody motion and, second, for theNbody problem. A way of increasing the number of degrees of freedom of a dynamical system is central to the method, and is the subject of an Appendix.
 Publication:

Celestial Mechanics
 Pub Date:
 October 1974
 DOI:
 10.1007/BF01227621
 Bibcode:
 1974CeMec..10..217H
 Keywords:

 Equations Of Motion;
 Gravitational Effects;
 Many Body Problem;
 Three Body Problem;
 Boundary Value Problems;
 Computer Programs;
 Hamiltonian Functions;
 Matrices (Mathematics);
 Numerical Analysis;
 Particle Collisions;
 Singularity (Mathematics);
 Transformations (Mathematics);
 Astronomy