Dirac reduction for nonholonomic mechanical systems and semidirect products
Dirac reduction for nonholonomic mechanical systems and semidirect products
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DOI：
10.1016/j.aam.2014.10.004
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发表时间：
2015-02-01
影响因子：
1.1
通讯作者：
Yoshimura, Hiroaki
中科院分区：
文献类型：
--
作者：
Gay-Balmaz, Francois;Yoshimura, Hiroaki
本文发展了对称性破缺李群上非完整系统的Dirac对称约化理论。减少进行狄拉克结构，以及相关的拉格朗日-狄拉克和汉密尔顿-狄拉克动力系统。这种减少过程是伴随着减少相关的变分结构的拉格朗日和哈密顿方面。所得到的约化动力系统称为带平流参数的隐式Euler-Poincare-Suslov方程和带平流参数的隐式Euler-Poisson-Suslov方程。该理论的说明与有限和无限维的例子的帮助。结果表明，二阶Rivlin-Ericksen流体的运动方程可以表示为一个无限维非完整系统。(C)2014爱思唯尔公司All rights reserved.
This paper develops the theory of Dirac reduction by symmetry for nonholonomic systems on Lie groups with broken symmetry. The reduction is carried out for the Dirac structures, as well as for the associated Lagrange-Dirac and Hamilton-Dirac dynamical systems. This reduction procedure is accompanied by reduction of the associated variational structures on both Lagrangian and Hamiltonian sides. The reduced dynamical systems obtained are called the implicit Euler-Poincare-Suslov equations with advected parameters and the implicit Euler-Poisson-Suslov equations with advected parameters. The theory is illustrated with the help of finite and infinite dimensional examples. It is shown that equations of motion for second order Rivlin-Ericksen fluids can be formulated as an infinite dimensional nonholonomic system in the framework of the present paper. (C) 2014 Elsevier Inc. All rights reserved.