变陀螺静动量的滚轮赛车:加速度判据和奇异吸引子

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2023-03-10 DOI:10.1134/S1560354723010070

Ivan A. Bizyaev, Ivan S. Mamaev

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引用次数: 0

摘要

本文研究了一类具有参数激励的非完整系统，即具有可变陀螺静动量的滚轮。我们详细地研究了能量无界增长(非保守费米加速度)的存在性问题。我们找到了一个判定轨迹存在的准则，其中一个速度分量在边界内增加并且具有渐近性\(t^{1/3}\)。此外，我们还表明，所考虑的问题可以简化为对三维庞卡罗图的分析。这个映射既展示了正则吸引子(不动点、极限环和环面)，也展示了奇异吸引子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Roller Racer with Varying Gyrostatic Momentum: Acceleration Criterion and Strange Attractors

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Roller Racer with Varying Gyrostatic Momentum: Acceleration Criterion and Strange Attractors

In this paper we investigate a nonholonomic system with parametric excitation, a Roller Racer with variable gyrostatic momentum. We examine in detail the problem of the existence of regimes with unbounded growth of energy (nonconservative Fermi acceleration). We find a criterion for the existence of trajectories for which one of the velocity components increases withound bound and has asymptotics \(t^{1/3}\). In addition, we show that the problem under consideration reduces to analysis of a three-dimensional Poincaré map. This map exhibits both regular attractors (a fixed point, a limit cycle and a torus) and strange attractors.

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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.