, Volume 163, Issue 2, pp 289-312
Date: 27 Oct 2005

Finiteness of relative equilibria of the four-body problem

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

We show that the number of relative equilibria of the Newtonian four-body problem is finite, up to symmetry. In fact, we show that this number is always between 32 and 8472. The proof is based on symbolic and exact integer computations which are carried out by computer.

Mathematics Subject Classification (2000)

70F10, 70F15, 37N05, 76Bxx