Celestial mechanics

, Volume 18, Issue 2, pp 165–184

Relative equilibrium solutions in the four body problem

  • Carles Simó

DOI: 10.1007/BF01228714

Cite this article as:
Simó, C. Celestial Mechanics (1978) 18: 165. doi:10.1007/BF01228714


Beyond the casen=3 little was known about relative equilibrium solutions of then-body problem up to recent years. Palmore's work provides in the general case much useful information. In the casen=4 he gives the totality of solutions when the four masses are equal and studies some degeneracies. We present here a survey of solutions for arbitrary masses, discussing the manifolds of degeneracy. The ordering of restricted potentials allows a counting of the number of bifurcation sets and different invariant manifolds. An analysis of linear stability is done in the restricted and general cases. As a result, values of the masses ensuring linear stability are given.

Copyright information

© D. Reidel Publishing Company 1978

Authors and Affiliations

  • Carles Simó
    • 1
  1. 1.Universitat Autònoma de BarcelonaBarcelonaSpain