Chaotic Dynamics and Stability Analysis of a Roller Bicycle

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2025-12-20 DOI:10.1134/S1560354725540032

Ivan A. Bizyaev, Anna S. Berdnikova

引用次数: 0

Abstract

We analyze the stability of the straight-line motion of the bicycle depending on the mass-geometric parameters of the bicycle and its translational velocity. We construct a region in phase space which corresponds to initial conditions under which the bicycle tends asymptotically to straight-line motion. To investigate the bifurcations of the periodic solutions of the system, we construct a chart of dynamical regimes on the plane of two parameters and a three-dimensional Poincaré map. We analyze the possibility of acceleration or deceleration of the bicycle when the angular velocity of the rotor periodically changes in time.

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轮式自行车混沌动力学及稳定性分析

根据自行车的质量几何参数及其平移速度，分析了自行车直线运动的稳定性。我们在相空间中构造了一个区域，该区域对应于自行车渐近趋于直线运动的初始条件。为了研究系统周期解的分岔，我们构造了一个双参数平面上的动力状态图和一个三维庞加莱图。分析了当转子角速度随时间周期性变化时，自行车加速或减速的可能性。

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

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.