A Restricted Four-body Problem for the Figure-eight Choreography

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2021-06-03 DOI:10.1134/S1560354721030023

Ricardo Lara, Abimael Bengochea

引用次数: 0

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.

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八字舞蹈的限制性四体问题

在本文中，我们引入了一个平面受限四体问题，其中一个无质量粒子在引力影响下运动，这是由于三个物体遵循数字8编排，并探索了该系统的一些非自治的对称周期轨道。我们利用逆对称性理论和数值研究了该系统的一类对称周期轨道。通过求解一些边值问题，计算了对称周期轨道(初始条件)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Regular and Chaotic Dynamics 物理-力学

CiteScore

2.50

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.