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Inventiones mathematicae

, Volume 163, Issue 2, pp 289–312 | Cite as

Finiteness of relative equilibria of the four-body problem

  • Marshall Hampton
  • Richard Moeckel
Article

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.

Keywords

Relative Equilibrium Integer Computation Exact Integer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA

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