On the rattleback dynamics

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:488

Article

Tudoran, Razvan M.¹  Girban, Anania² 

[1] West Univ Timisoara, Fac Math & Comp Sci, Dept Math, Blvd Vasile Parvan 4, Timisoara 300223, Romania

[2] Politehn Univ Timisoara, Dept Math, Piata Victoriei 2, Timisoara 300006, Romania

关键词: Equilibria;    Periodic orbits;    Heteroclinic orbits;    Energy-Casimir mapping;    Stability;    Asymptotic stabilization;   

DOI  :  10.1016/j.jmaa.2020.124066

来源: Elsevier

【 摘 要 】

In this paper we present some relevant dynamical properties of an idealized conservative model of the rattleback, from the Poisson dynamics point of view. In the first half of the article, along with a dynamical study of the orbits, using a Hamilton-Poisson realization of the dynamical system, we provide a geometric characterization of the space of orbits in terms of Whitney stratifications associated to the image of the energy-Casimir mapping. In the second half of the article we provide an explicit method to stabilize asymptotically any arbitrary fixed orbit/cycle of the rattleback system and to keep unchanged the geometry of the model space. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free