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Abstract: In this paper we present a complete classification of the isolated centralconfigurations of the five-body problem with equal masses. This is accomplishedby using the polyhedral homotopy method to approximate all the isolatedsolutions of the Albouy-Chenciner equations. The existence of exact solutions,in a neighborhood of the approximated ones, is then verified using the Krawczykmethod. Although the Albouy-Chenciner equations for the five-body problem arehuge, it is possible to solve them in a reasonable amount of time.



Author: Tsung-Lin Lee, Manuele Santoprete

Source: https://arxiv.org/



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