Periodic flows, rank-two Poisson structures, and nonholonomic mechanics

被引：27

作者：

Fassò, F ^{[1
]}

Giacobbe, A ^{[1
]}

Sansonetto, N ^{[1
]}

机构：

[1] Univ Padua, Dipartimento Matemat Pura & Applicata, I-35131 Padua, Italy

来源：

REGULAR & CHAOTIC DYNAMICS | 2005年 / 10卷 / 03期

基金：

美国国家科学基金会; 中国国家自然科学基金; 欧洲研究理事会; 欧盟地平线“2020”;

关键词：

Poisson structures; non-holonomic systems; periodic flows;

D O I：

10.1070/RD2005v010n03ABEH000315

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It has been recently observed that certain (reduced) nonholonomic systems are Hamiltonian with respect to a rank-two Poisson structure. We link the existence of these structures to a dynamical property of the (reduced) system: its periodicity, with positive period depending continuously on the initial data. Moreover, we show that there are in fact infinitely many such Poisson structures and we classify them. We illustrate the situation on the sample case of a heavy ball rolling on a surface of revolution.

引用

页码：267 / 284

页数：18

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