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arXiv · 2207.04413

A numerical analysis of planar central and balanced configurations in the (n+1)-body problem with a small mass

Alexandru Doicu·Lei Zhao·Adrian Doicu
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Abstract

Two numerical algorithms for analyzing planar central and balanced configurations in the $(n+1)$-body problem with a small mass are presented. The first one relies on a direct solution method of the $(n+1)$-body problem by using a stochastic optimization approach, while the second one relies on an analytic-continuation method, which involves the solutions of the $n$-body and the restricted $(n+1)$-body problem, and the application of a local search procedure to compute the final $(n+1)$-body configuration in the neighborhood of the configuration obtained at the first two steps. Some exemplary central and balanced configurations in the cases $n=4,5,6$ are shown.

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Alexandru Doicu, Lei Zhao, Adrian Doicu. 2022-07-10. A numerical analysis of planar central and balanced configurations in the (n+1)-body problem with a small mass. https://arxiv.org/abs/2207.04413

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