论文标题
带有阿贝尔对称组的隐式拉格朗日系统的离散狄拉克降低
Discrete Dirac reduction of implicit Lagrangian systems with abelian symmetry groups
论文作者
论文摘要
本文开发了离散的狄拉克（Dirac）降低离散lagrange-dirac系统的理论，其作用于配置空间。我们从线性理论开始，然后使用缩回兼容图表将其扩展到非线性设置。我们考虑减少离散的狄拉克结构和离散的拉格朗日 - 五键原则，并表明它们都导致了相同的离散lagrange-poincaré-dirac方程。离散缩小空间的协调依赖于主束上离散连接的概念。最后，我们通过将其应用于磁场中的带电粒子以及双球形摆上获得的方法。
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-Poincaré-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.
