Celestial Mechanics and Dynamical Astronomy

, Volume 124, Issue 2, pp 145–153 | Cite as

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

  • Marshall Hampton
Original Article


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 \(N+1\)-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.


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


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of Minnesota, DuluthDuluthUSA

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