Discrete Dirac reduction of implicit Lagrangian systems with abelian symmetry groups

被引:2
|
作者
Rodriguez Abella, Alvaro [1 ]
Leok, Melvin [2 ]
机构
[1] UAM, CSIC, UC3M, Inst Ciencias Matemat,UCM, Calle Nicolas Cabrera 13-15, Madrid, Spain
[2] Univ Calif San Diego, Dept Math, 9500 Gilman Dr, La Jolla, CA 92093 USA
来源
JOURNAL OF GEOMETRIC MECHANICS | 2023年 / 15卷 / 01期
关键词
discrete mechanical systems; geometric numerical integration; Lagrange-Poincare-Dirac equations; reduction by symmetries; VARIATIONAL INTEGRATORS; EULER-POINCARE; LIE; MECHANICS; DISCRETIZATION;
D O I
10.3934/jgm.2023013
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper develops the theory of discrete Dirac reduction of discrete Lagrange-Dirac systems with an abelian symmetry group acting on the configuration space. We begin with the linear theory and, then, we extend it to the nonlinear setting using retraction compatible charts. We consider the reduction of both the discrete Dirac structure and the discrete Lagrange-Pontryagin principle, and show that they both lead to the same discrete Lagrange-Poincar ' e-Dirac equations. The coordinatization of the discrete reduced spaces relies on the notion of discrete connections on principal bundles. At last, we demonstrate the method obtained by applying it to a charged particle in a magnetic field, and to the double spherical pendulum.
引用
收藏
页码:319 / 356
页数:38
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