Existence of symmetric central configurations
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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.
Keywordsn-Body problem Balanced configurations Relative equilibria Orbit types Symmetric variational problems
Mathematics Subject Classification70F10 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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