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Journal of Dynamics and Differential Equations

, Volume 31, Issue 4, pp 2053–2060 | Cite as

On Centered Co-circular Central Configurations of the n-Body Problem

  • Montserrat CorberaEmail author
  • Claudia Valls
Article
  • 56 Downloads

Abstract

We study the co-circular central configurations of the n-body problem for which the center of mass and the center of the common circle coincide. In particular, we prove that there are no central configurations of this type with all the masses equal except one. This provides more evidences for the veracity of the conjecture that the regular n-gon with equal masses is the unique co-circular central configuration of the n-body problem whose center of mass is the center of the circle. Our result remains valid if we consider power-law potentials.

Keywords

Co-circular central configurations n-Body problem Regular n-gon 

Mathematics Subject Classification

70F07 70F15 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Facultat de Ciències i TecnologiaUniversitat de Vic - Universitat Central de Catalunya (UVic-UCC)VicSpain
  2. 2.Departamento de Matemàtica, Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal

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