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 figure-eight
choreography, and explore some symmetric periodic orbits of this system which turns out to
be nonautonomous. We use reversing symmetries to study both theoretically and numerically a
certain type of symmetric periodic orbits of this system. The symmetric periodic orbits (initial
conditions) were computed by solving some boundary-value problems.
The first author is pleased to acknowledge the financial support of Instituto Tecnológico
Autónomo de México (ITAM). The second author is pleased to acknowledge the support of
Asociación Mexicana de Cultura A.C., the National System of Researchers (SNI), and Conacyt-México Project A1S10112.
\Bibitem{LarBen21}
\by Ricardo Lara, Abimael Bengochea
\paper A Restricted Four-body Problem
for the Figure-eight Choreography
\jour Regul. Chaotic Dyn.
\yr 2021
\vol 26
\issue 3
\pages 222--235
\mathnet{http://mi.mathnet.ru/rcd1112}
\crossref{https://doi.org/10.1134/S1560354721030023}
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Linking options:
https://www.mathnet.ru/eng/rcd1112
https://www.mathnet.ru/eng/rcd/v26/i3/p222
This publication is cited in the following 2 articles:
Abimael Bengochea, Jaime Burgos-García, Ernesto Pérez-Chavela, “Symmetric periodic orbits near binary collision in a restricted four-body problem for the figure-eight choreography”, Celest Mech Dyn Astron, 136:5 (2024)
Xi Zheng, “3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System”, Applied Mathematics and Nonlinear Sciences, 8:1 (2023), 427
Citation in format AMSBIB
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