Nonholonomic versus vakonomic dynamics on a Riemann–Cartan manifold
Nonholonomic versus vakonomic dynamics on a Riemann–Cartan manifold
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DOI：
10.1063/1.1928708
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发表时间：
2005-06
影响因子：
1.3
通讯作者：
Yongxin Guo;Yong Wang;G. Chee;F. Mei
中科院分区：
文献类型：
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作者：
Yongxin Guo;Yong Wang;G. Chee;F. Mei
对于Chaplygin非完整约束系统，通过非完整映射到黎曼流形，可以使约束流形具有黎曼-卡尔坦几何结构。在黎曼-卡尔坦几何的框架下，比较了现有的两种动力学：非完整动力学和非完整动力学。证明了黎曼-卡坦约束流形上的自平行运动方程和测地运动方程分别可以用来描述非完整动力学和非完整动力学的运动方程。如果满足Riemann-Cartan连接的度量性条件，则Riemann-Cartan流形的扭转（扭曲）表征了自平行轨迹与测地轨迹的区别以及非完整方程与非完整方程的区别。
For the Chaplygin’s nonholonomic constrained systems, the constraint manifold can be endowed with Riemann–Cartan geometric structure by nonholonomic mapping into a Riemann manifold. The two kinds of existing dynamics, nonholonomic dynamics and vakonomic dynamics, are compared in the framework of Riemann–Cartan geometry. It is proved that the equations of motion for nonholonomic and vakonomic dynamics are described by the equations of autoparallel and geodesic trajectories on the Riemann–Cartan constraint manifold, respectively. If the metricity condition of Riemann–Cartan connection is satisfied, the torsion (contorsion) of the Riemann–Cartan manifold characterizes the difference between the autoparallel and geodesic trajectories as well as the distinction between the nonholonomic and vakonomic equations.