Existence of symmetric central configurations

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    Central configurations have been of great interest overmany 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.
    Original languageEnglish
    Pages (from-to)405-418
    JournalCelestial Mechanics and Dynamical Astronomy
    Issue number4
    Publication statusPublished - 10 Jun 2015


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


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