用双四元数统一双曲和球面 $$2$ 天体问题

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2023-12-07 DOI:10.1134/S1560354723060011

Philip Arathoon

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引用次数: 0

摘要

球面上的（2）体问题和双曲空间上的（2）体问题都是定义在复球面上的全形哈密顿系统的实数形式。这允许我们用双四元数进行自然描述，并允许我们通过复数化双曲系统并将其视为球面系统的复数化来解决有关双曲系统的问题。这样，球面上的（2\）体问题的结果就很容易转换到双曲面上。例如，我们利用这一思想对双曲 3 空间上的$2$-体问题的相对均衡进行了完全分类，并讨论了它们在严格吸引力势下的稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$Unifying the Hyperbolic and Spherical $2$-Body Problem with Biquaternions$

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Unifying the Hyperbolic and Spherical $2$-Body Problem with Biquaternions

The $2$-body problem on the sphere and hyperbolic space are both real forms of holomorphic Hamiltonian systems defined on the complex sphere. This admits a natural description in terms of biquaternions and allows us to address questions concerning the hyperbolic system by complexifying it and treating it as the complexification of a spherical system. In this way, results for the $2$-body problem on the sphere are readily translated to the hyperbolic case. For instance, we implement this idea to completely classify the relative equilibria for the $2$-body problem on hyperbolic 3-space and discuss their stability for a strictly attractive potential.

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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.