Integrability in a Nonlinear Model of Swing Oscillatory Motion

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

引用次数: 0

Abstract

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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摆振运动非线性模型的可积性

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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来源期刊

Journal of Geometry and Symmetry in Physics PHYSICS, MATHEMATICAL-

CiteScore

1.50

自引率

25.00%

发文量

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