中国物理B ›› 2004, Vol. 13 ›› Issue (12): 2182-2186.doi: 10.1088/1009-1963/13/12/036
• • 上一篇
黄飞江1, 卢一兵1, 罗绍凯2
Luo Shao-Kai (罗绍凯)ab, Huang Fei-Jiang (黄飞江)b, Lu Yi-Bing (卢一兵)b
摘要: For a nonholonomic system, a new type of Lie symmetrical non-Noether conserved quantity is given under general infinitesimal transformations of groups in which time is variable. On the basis of the invariance theory of differential equations of motion under infinitesimal transformations for t and q_s, we construct the Lie symmetrical determining equations, the constrained restriction equations and the additional restriction equations of the system. And a new type of Lie symmetrical non-Noether conserved quantity is directly obtained from the Lie symmetry of the system, which only depends on the variables t, q_s and \dot{q}_s. A series of deductions are inferred for a holonomic nonconservative system, Lagrangian system and other dynamical systems in the case of vanishing of time variation. An example is given to illustrate the application of the results.
中图分类号: (Lie algebras of Lie groups)