A new type of Lie symmetrical non-Noether conserved quantity for nonholonomic systems
Luo Shao-Kai (罗绍凯)ab, Huang Fei-Jiang (黄飞江)b, Lu Yi-Bing (卢一兵)b
a Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang University of Sciences, Hangzhou 310018, China; b Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003, ChinaInstitute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003, China
Abstract 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.
Received: 02 March 2004
Revised: 23 August 2004
Accepted manuscript online:
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10372053), the Natural Science Foundation of Hunan Province (Grant No 03JJY3005), and the Scientific Research Foundation of the Education Bureau of Hunan Province, China (Gran
Cite this article:
Luo Shao-Kai (罗绍凯), Huang Fei-Jiang (黄飞江), Lu Yi-Bing (卢一兵) A new type of Lie symmetrical non-Noether conserved quantity for nonholonomic systems 2004 Chinese Physics 13 2182
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