A stochastic optimization algorithm for analyzing planar central and balanced configurations in the n-body problem

2020/10/29 by Alexandru Doicu, Lei Zhao, Doicu, Alexandru +3
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #GNSS positioning and interference #Numerical Analysis (math.NA) #Spacecraft Dynamics and Control #Stellar, planetary, and galactic studies #cs.NA #math.DS #math.NA

paper · pdf · doi:10.48550/arxiv.2010.15358

37 pages, 13 figures, 2 tables

openalex publication_date 2020/10/29 · arxiv created 2020/12/23 · arxiv updated 2020/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A stochastic optimization algorithm for analyzing planar central and balanced configurations in the n-body problem is presented. We find a comprehensive list of equal mass central configurations satisfying the Morse equality up to n=12. We show some exemplary balanced configurations in the case n=5, as well as some balanced configurations without any axis of symmetry in the cases n=4 and n=10.

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