Inventiones mathematicae

, Volume 163, Issue 2, pp 289–312

Finiteness of relative equilibria of the four-body problem

Authors

    • School of MathematicsUniversity of Minnesota
    • School of MathematicsUniversity of Minnesota
Article

DOI: 10.1007/s00222-005-0461-0

Cite this article as:
Hampton, M. & Moeckel, R. Invent. math. (2006) 163: 289. doi:10.1007/s00222-005-0461-0

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.

Supplementary material

Copyright information

© Springer-Verlag 2005