A new non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations
Luo Shao-Kai (罗绍凯)abd, Cai Jian-Le (蔡建乐)c, Jia Li-Qun (贾利群)d
a Institute of Mathematical Mechanics and Mathematical Physics,Zhejiang Science-Technology University, Hangzhou 310018, China; b Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003 China; c Department of Physics, Hangzhou Teachers College, Hangzhou 310018, Chinad Science College of Southern, Yangtze University, Wuxi 214063, China
Abstract For the relativistic holonomic nonconservative system, a new Lie symmetrical non-Noether conserved quantity is given under general infinitesimal transformations of groups in which time is variable. On the basis of the theory of invariance of differential equations of motion under infinitesimal transformations for $t$ and $q_s$, we construct the relativistic Lie symmetrical determining equations and obtain directly a new relativistic Lie symmetrical non-Noether conserved quantity of the system, which only depend on the variables $t$, $q_s$ and $\dot{q}_s$. An example is given to illustrate the application of the results.
Received: 21 June 2004
Revised: 15 December 2004
Accepted manuscript online:
(General theory of classical mechanics of discrete systems)
Fund: Project supported by National Natural Science Foundation of China (Grant No 10372053), the Natural Science Foundation of Hunan Province (Grant No 03JJY3005) and Scientific Research Foundation of Education Bureau of Hunan Province (Grant No 02C033).
Cite this article:
Luo Shao-Kai (罗绍凯), Cai Jian-Le (蔡建乐), Jia Li-Qun (贾利群) A new non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations 2005 Chinese Physics 14 656
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