DIRAC STRUCTURES AND HAMILTON-JACOBI THEORY FOR LAGRANGIAN MECHANICS ON LIE ALGEBROIDS

被引：10

作者：

Leok, Melvin ^{[1
]}

Sosa, Diana ^{[2
,3
,4
]}

机构：

[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

[2] Univ La Laguna, Fac CC EE & Empresariales, Dept Econ Aplicada, Tenerife, Canary Islands, Spain

[3] Univ La Laguna, Fac CC EE & Empresariales, Unidad Asociada ULL CSIC Geometria Diferencial &, Tenerife, Canary Islands, Spain

[4] Univ Europea Canarias, Tenerife, Canary Islands, Spain

来源：

JOURNAL OF GEOMETRIC MECHANICS | 2012年 / 4卷 / 04期

基金：

美国国家科学基金会;

关键词：

Dirac structures; implicit Lagrangian systems; Lie algebroids; Lagrangian mechanics; nonholonomic systems; Hamilton-Jacobi equation; SYSTEMS; FORMULATION; REDUCTION; FRAMEWORK; DYNAMICS; EQUATION;

D O I：

10.3934/jgm.2012.4.421

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper develops the notion of implicit Lagrangian systems on Lie algebroids and a Hamilton-Jacobi theory for this type of system. The Lie algebroid framework provides a natural generalization of classical tangent bundle geometry. We define the notion of an implicit Lagrangian system on a Lie algebroid E using Dirac structures on the Lie algebroid prolongation (TE)-E-E*. This setting includes degenerate Lagrangian systems with nonholonomic constraints on Lie algebroids.

引用

页码：421 / 442

页数：22

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