A restricted four-body problem for the eight figure choreography

2019/10/28 by Ricardo Lara, Lara, Ricardo, Abimael Bengochea +1
Engineering · #45.50.-j #45.50.Pk #95.10.Ce #Dynamical Systems (math.DS) #FOS: Mathematics #Guidance and Control Systems #Space Satellite Systems and Control #Spacecraft Dynamics and Control

paper · pdf · doi:10.48550/arxiv.1910.12822

openalex publication_date 2019/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we introduce a planar restricted four-body problem where a massless particle moves under the gravitational influence due to three bodies following the eight figure choreography, and we explore some symmetric periodic orbits of this system which turns out to be non autonomous. We demonstrate that certain families of involutions are reversing symmetries of certain N-body problem. We consider a particular case of such families of reversing symmetries and we use it to study both theoretically and numerically certain type of symmetric periodic orbits of this system. The symmetric periodic orbits (initial conditions) were determined by means of solving some boundary value problems.

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