## 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 language | English (US) |
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Pages (from-to) | 145-153 |

Number of pages | 9 |

Journal | Celestial Mechanics and Dynamical Astronomy |

Volume | 124 |

Issue number | 2 |

DOIs | |

State | Published - Feb 1 2016 |

## Keywords

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