Isolating blocks near the collinear relative equilibria of the three-body problem

Richard Moeckel

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

The collinear relative equilibrium solutions are among the few explicitly known periodic solutions of the Newtonian three-body problem. When the energy and angular momentum constants are varied slightly, these unstable periodic orbits become normally hyperbolic invariant spheres whose stable and unstable manifolds form separatrices in the integral manifolds. The goal of this paper is to construct simple isolating blocks for these invariant spheres analogous to those introduced by Conley in the restricted three-body problem. This allows continuation of the invariant set and the separatrices to energies and angular momenta far from those of the relative equilibrium.

Original languageEnglish (US)
Pages (from-to)4395-4425
Number of pages31
JournalTransactions of the American Mathematical Society
Volume356
Issue number11
DOIs
StatePublished - Nov 1 2004

Keywords

  • Celestial mechanics
  • Central configurations
  • Three-body problem

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