Splendid isolation: local uniqueness of the centered co-circular relative equilibria in the N-body problem

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Abstract

We study the neighborhood of the equal mass regular polygon relative equilibria in the N-body probem, and show that this relative equilibirum is isolated among the co-circular configurations (in which each point lies on a common circle) for which the center of mass is located at the center of the common circle. It is also isolated in the sense that a sufficiently small mass cannot be added to the common circle to form a (Formula presented.) -body relative equilibrium. These results provide strong evidence for a conjecture that the equal mass regular polygon is the only co-circular relative equilibrium with its center of mass located at the center of the common circle.

Original languageEnglish (US)
Pages (from-to)145-153
Number of pages9
JournalCelestial Mechanics and Dynamical Astronomy
Volume124
Issue number2
DOIs
StatePublished - Feb 1 2016

Keywords

  • Central configurations
  • Choreographies
  • Co-circular configurations
  • Equal mass regular polygon
  • N-body problem
  • Relative equilibria

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