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

2022/07/10 by Alexandru Doicu, Lei Zhao, Doicu, Alexandru +3
Engineering · Physics and Astronomy · #Astro and Planetary Science #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical Analysis (math.NA) #Spacecraft Dynamics and Control #Stellar, planetary, and galactic studies

paper · pdf · doi:10.48550/arxiv.2207.04413

openalex publication_date 2022/07/10 · openalex created_date 2022/07/13 · openalex updated_date 2026/07/28

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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