Hamiltonization of Solids of Revolution Through Reduction

被引：11

作者：

Balseiro, Paula ^{[1
]}

机构：

[1] Univ Fed Fluminense, Inst Matemat & Estat, Rua Prof Marcos Waldemar de Freitas Reis,S-N, BR-24020140 Niteroi, RJ, Brazil

来源：

JOURNAL OF NONLINEAR SCIENCE | 2017年 / 27卷 / 06期

关键词：

Geometric mechanics; Nonholonomic systems; Hamiltonization; (almost) Poisson brackets; Reduction by symmetries; NONHOLONOMIC MECHANICAL SYSTEMS; CONSERVATION-LAWS; POISSON STRUCTURES; NOETHER THEOREM; DYNAMICS; SYMMETRY; GEOMETRY; HIERARCHY; BRACKETS;

D O I：

10.1007/s00332-017-9394-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the relation between conserved quantities of nonholonomic systems and the hamiltonization problem employing the geometric methods of Balseiro (Arch Ration Mech Anal 214:453-501, 2014) and Balseiro and Garcia-Naranjo (Arch Ration Mech Anal 205(1):267-310, 2012). We illustrate the theory with classical examples describing the dynamics of solids of revolution rolling without sliding on a plane. In these cases, using the existence of two conserved quantities we obtain, by means of gauge transformations and symmetry reduction, genuine Poisson brackets describing the reduced dynamics.

引用

页码：2001 / 2035

页数：35

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