Orbits near central configurations for four equal masses
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This study relates to equal-mass four-body orbits close to a quadruple central configuration. Locally, these orbits can be approximated by a perturbation from the homothetic quadruple collision/expansion orbit. Appropriate expressions are derived and the equal-mass four-body Siegel exponents and associated eigenmodes are presented.
KeywordsCentral configurations Relative equilibria Four-body problem Siegel exponents Eigenmodes
The author is grateful to Douglas Heggie and the University of Edinburgh and Bonnie Steves and Glasgow Caledonian University for their hospitality while progressing this research. He also thanks the organisers and participants of Celmec VI: San Martino al Cimino, Viterbo, Italy for fruitful discussions and the referees of this paper for their constructive comments.
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