Regularizable collinear periodic solutions in the n-body problem with arbitrary masses

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-11 DOI:10.1016/j.aim.2024.109947

Guowei Yu

引用次数: 0

Abstract

For n-body problem with arbitrary positive masses, we prove there are regularizable collinear periodic solutions for any ordering of the masses, going from a simultaneous binary collision to another in half of a period with half of the masses moving monotonically to the right and the other half monotonically to the left. When the masses satisfy certain equality condition, the solutions have extra symmetry. This also gives a new proof of the existence of Schubart orbit, when $n = 3$ .

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具有任意质量的 n 体问题中可规整的共线周期解

对于具有任意正质量的 n 体问题，我们证明了对于质量的任意排序都存在可正则化的碰撞周期解，从同时发生的二元碰撞到另一组碰撞只需半个周期，其中一半质量单调地向右移动，另一半质量单调地向左移动。当质量满足某些相等条件时，解具有额外的对称性。这也给出了 n=3 时舒巴特轨道存在的新证明。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.