On the dynamics of the Craik–Okamoto and the Euler top

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2025-05-03 DOI:10.1016/j.physd.2025.134684

Jaume Llibre , Claudia Valls

引用次数: 0

Abstract

We study the dynamics of the Craik–Okamoto system and its relation with the dynamics of the Euler top. We show that both systems exhibit the same dynamics in a neighborhood of infinity and we describe completely the phase portraits of the Euler top. Additionally we provide explicitly the Euler top solutions in function of the time. We show that the orbits given by the invariant straight lines of the Craik–Okamoto system are in fact center manifolds of equilibrium points at infinity. Moreover, we show that while in the Euler top all the orbits lie on invariant algebraic surfaces, in the Craik–Okamoto system any orbit is on an invariant algebraic surface.

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关于Craik-Okamoto和欧拉顶的动力学

研究了Craik-Okamoto系统的动力学及其与欧拉顶动力学的关系。我们证明了这两个系统在无穷邻域中表现出相同的动力学，并完整地描述了欧拉顶的相图。此外，我们还明确地给出了随时间变化的欧拉顶解。我们证明了克雷克-冈本系统的不变直线所给出的轨道实际上是无穷远处平衡点的中心流形。此外，我们证明了在欧拉顶中，所有轨道都在不变代数曲面上，而在Craik-Okamoto系统中，任何轨道都在不变代数曲面上。

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

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.