Existence of symmetric central configurations

Montaldi, James (2015) Existence of symmetric central configurations. Celestial Mechanics and Dynamical Astronomy. ISSN 0923-2958 (In Press)

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Abstract

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.

Item Type:	Article
Uncontrolled Keywords:	n-body problem, balanced configurations, relative equilibria, orbit types, symmetric variational problems
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 70 Mechanics of particles and systems
Depositing User:	Dr James Montaldi
Date Deposited:	29 May 2015
Last Modified:	20 Oct 2017 14:13
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2269

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