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Periodic Solutions for Circular Restricted 4-body Problems with Newtonian Potentials

2013/01/04 by Xiaoxiao Zhao, Zhao, Xiaoxiao, Shiqing Zhang +1
Engineering · Physics and Astronomy · #Astro and Planetary Science #FOS: Physical sciences #Mathematical Physics (math-ph) #Space Satellite Systems and Control #Spacecraft Dynamics and Control

paper · pdf · doi:10.48550/arxiv.1301.0767

openalex publication_date 2013/01/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study the existence of non-collision periodic solutions with Newtonian potentials for the following planar restricted 4-body problems: Assume that the given positive masses m1,m2,m3 in a Lagrange configuration move in circular obits around their center of masses, the sufficiently small mass moves around some body. Using variational minimizing methods, we prove the existence of minimizers for the Lagrangian action on anti-T/2 symmetric loop spaces. Moreover, we prove the minimizers are non-collision periodic solutions with some fixed wingding numbers.

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