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

07/10/2022

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by   Alexandru Doicu, et al.

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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.