Celestial Mechanics and Dynamical Astronomy

, Volume 122, Issue 4, pp 405–418 | Cite as

Existence of symmetric central configurations

  • James Montaldi
Original Article


Central configurations have been of great interest over many years, with the earliest examples due to Euler and Lagrange. There are numerous results in the literature demonstrating the existence of central configurations with specific symmetry properties, using slightly different techniques in each. The aim here is to describe a uniform approach by adapting to the symmetric case the well-known variational argument showing the existence of central configurations. The principal conclusion is that there is a central configuration for every possible symmetry type, and for any symmetric choice of masses. Finally the same argument is applied to the class of balanced configurations introduced by Albouy and Chenciner.


n-Body problem Balanced configurations Relative equilibria Orbit types Symmetric variational problems 

Mathematics Subject Classification

70F10 70G65 



I would like to thank Manuele Santoprete for pointing out some references, and Alain Albouy for making a number of helpful suggestions.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.University of ManchesterManchesterUK

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