摆振运动非线性模型的可积性

IF 0.5 Q4 PHYSICS, MATHEMATICAL

Journal of Geometry and Symmetry in Physics Pub Date : 2023-03-30 DOI:10.7546/jgsp-65-2023-93-108

S. Nikolov, V. Vassilev

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引用次数: 0

摘要

非线性动力系统可以从许多不同的方向进行研究：i）~寻找可积情况及其解析解，ii）~研究可积性的代数性质，iii）~可积系统的拓扑分析，等等。本文的目的是找到一个动力学系统的可积情况，该系统将骑车人和秋千（从坐姿）描述为复摆。根据我们的分析计算结果，我们可以得出这个系统有两种可积的情况：1）~哑铃长度和点质量满足一个特殊条件；2） ~忽略了重力。

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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Integrability in a Nonlinear Model of Swing Oscillatory Motion

Nonlinear dynamical systems can be studied in many different directions: i)~finding integrable cases and their analytical solutions, ii)~investigating the algebraic nature of the integrability, iii)~topological analysis of integrable systems, and so on. The aim of the present paper is to find integrable cases of a dynamical system describing the rider and the swing pumped (from the seated position) as a compound pendulum. As a result of our analytical calculations, we can conclude that this system has two integrable cases when: 1)~the dumbbell lengths and point-masses meet a special condition; 2)~the gravitational force is neglected.

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来源期刊

Journal of Geometry and Symmetry in Physics PHYSICS, MATHEMATICAL-

CiteScore

1.50

自引率

25.00%

发文量

期刊介绍： The Journal of Geometry and Symmetry in Physics is a fully-refereed, independent international journal. It aims to facilitate the rapid dissemination, at low cost, of original research articles reporting interesting and potentially important ideas, and invited review articles providing background, perspectives, and useful sources of reference material. In addition to such contributions, the journal welcomes extended versions of talks in the area of geometry of classical and quantum systems delivered at the annual conferences on Geometry, Integrability and Quantization in Bulgaria. An overall idea is to provide a forum for an exchange of information, ideas and inspiration and further development of the international collaboration. The potential authors are kindly invited to submit their papers for consideraion in this Journal either to one of the Associate Editors listed below or to someone of the Editors of the Proceedings series whose expertise covers the research topic, and with whom the author can communicate effectively, or directly to the JGSP Editorial Office at the address given below. More details regarding submission of papers can be found by clicking on "Notes for Authors" button above. The publication program foresees four quarterly issues per year of approximately 128 pages each.