KINEMATIC REDUCTION AND THE HAMILTON-JACOBI EQUATION

被引：18

作者：

Barbero-Linan, Maria ^{[1
,2
]}

de Leon, Manuel ^{[2
]}

Martin de Diego, David ^{[2
]}

Marrero, Juan C. ^{[3
]}

Munoz-Lecanda, Miguel C. ^{[4
]}

机构：

[1] Univ Carlos III Madrid, Dept Matemat, Madrid 28911, Spain

[2] Inst Ciencias Matemat CSIC UAM UC3M UCM, Madrid 28049, Spain

[3] Univ La Laguna, Fac Matemat, Dept Matemat Fundamental, Unidad Asociada ULL CSIC, Tenerife 38071, Canary Islands, Spain

[4] Dept Matemat Aplicada IV, Barcelona 08034, Spain

来源：

JOURNAL OF GEOMETRIC MECHANICS | 2012年 / 4卷 / 03期

关键词：

Skew-symmetric algebroids; Hamilton-Jacobi equation; mechanical control systems; decoupling vector fields; kinematic reduction; LIE ALGEBROIDS; LAGRANGIAN MECHANICS; SYSTEMS; INTEGRABILITY;

D O I：

10.3934/jgm.2012.4.207

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new mathematical techniques for mechanics de fined on a skew-symmetric algebroid. This geometric structure allows us to describe in a simplified way the mechanics of nonholonomic systems with both control and external forces.

引用

页码：207 / 237

页数：31

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