机械系统中的度量几何和强迫振荡

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2025-08-11 DOI:10.1134/S1560354725040173

Ivan Yu. Polekhin

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引用次数: 0

摘要

考虑黎曼流形上存在强迫振荡的问题，黎曼流形上的度规由机械系统的动能定义。在假定广义力是时间的周期函数的前提下，我们找到了同周期的周期解。我们给出了这些解存在的充分条件，这些解本质上依赖于相应黎曼流形上测地线的行为。

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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Metric Geometry and Forced Oscillations in Mechanical Systems

We consider the problem of existence of forced oscillations on a Riemannian manifold, the metric on which is defined by the kinetic energy of a mechanical system. Under the assumption that the generalized forces are periodic functions of time, we find periodic solutions of the same period. We present sufficient conditions for the existence of such solutions, which essentially depend on the behavior of geodesics on the corresponding Riemannian manifold.

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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.