Periodic orbits near collision in a restricted four-body problem for the eight choreography

2024/04/01 by Abimael Bengochea, Bengochea, Abimael, Jaime Burgos–García +3
Engineering · Physics and Astronomy · #45.50.-j #45.50.Pk #95.10.Ce #Astro and Planetary Science #Dynamical Systems (math.DS) #FOS: Mathematics #Space Satellite Systems and Control #Spacecraft Dynamics and Control

paper · pdf · doi:10.48550/arxiv.2404.01463

openalex publication_date 2024/04/01 · openalex created_date 2024/04/05 · openalex updated_date 2026/07/28

Abstract

We study orbits near collision in a non-autonomous restricted planar four-body problem. This restricted problem consists of a massless particle moving under the gravitational influence due to three bodies following the figure-eight choreography. We use regularized coordinates in order to deal numerically with motions near collision, and reversing symmetries to study both theoretically and numerically certain type of symmetric periodic orbits of the restricted system. The symmetric periodic orbits (initial conditions) were computed with the help of some boundary-value problems.

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