A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries

被引：9

作者：

Balseiro, Paula ^{[1
]}

Sansonetto, Nicola ^{[2
]}

机构：

[1] Univ Fed Fluminense, Inst Matemat, Rua Mario Santos Braga S-N, BR-24020140 Rio De Janeiro, Brazil

[2] Univ Padua, Dipartimento Matemat, Via Trieste 64, I-35121 Padua, Italy

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2016年 / 12卷

关键词：

nonholonomic systems; Lie group symmetries; first integrals; gauge symmetries; and gauge momenta; MECHANICAL SYSTEMS; CONSERVATION-LAWS; NOETHER THEOREM; REDUCTION; HIERARCHY; BRACKETS; BALL;

D O I：

10.3842/SIGMA.2016.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the existence of first integrals in nonholonomic systems with symmetry. First we define the concept of M -cotangent lift of a vector field on a manifold Q in order to unify the works [Balseiro P., Arch. Ration. Mech. Anal. 214 (2014), 453-501, arXiv:1301.1091], [Fosse F., Ramos A., Sansonetto N., Regul. Chaotic Dyn. 12 (2007), 579588], and [Fosse F., Giacobbe A., Sansonetto N., Rep. Math. Phys. 62 (2008), 345-367]. Second, we study gauge symmetries and gauge momenta, in the cases in which there are the symmetries that satisfy the so-called vertical symmetry condition. Under such condition we can predict the number of linearly independent first integrals (that are gauge momenta). We illustrate the theory with two examples.

引用

页数：14

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