关于常曲率空间中两个粒子质心的一些注释

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-09-28 DOI:10.3934/jgm.2020020

Luis C. Garc'ia-Naranjo

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引用次数: 1

摘要

通过回顾Galperin [Comm. Math]提出的“杠杆的相对论性规则”的概念，讨论了恒定高斯曲率二维空间中两个粒子质心的概念。物理学报，154(1993)，63—84]，并将其与其他两种自然产生的质心定义进行比较，这两种定义是在处理常曲率空间中的二体问题时自然产生的:首先是作为初始静止粒子的碰撞点，其次是作为稳定旋转解的旋转中心。结果表明，如果粒子具有不同的质量，那么这些定义只有在曲率消失的情况下才等效，而在一般情况下导致三种不同的质心概念。

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Some remarks about the centre of mass of two particles in spaces of constant curvature

The concept of centre of mass of two particles in 2D spaces of constant Gaussian curvature is discussed by recalling the notion of "relativistic rule of lever" introduced by Galperin [Comm. Math. Phys. 154 (1993), 63--84] and comparing it with two other definitions of centre of mass that arise naturally on the treatment of the 2-body problem in spaces of constant curvature: firstly as the collision point of particles that are initially at rest, and secondly as the centre of rotation of steady rotation solutions. It is shown that if the particles have distinct masses then these definitions are equivalent only if the curvature vanishes and instead lead to three different notions of centre of mass in the general case.

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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.