Momentum-dependent symmetries and non-Noether conserved quantities for nonholonomic nonconservative Hamilton canonical systems
Fu Jing-Li (傅景礼)acd, Chen Li-Qun (陈立群)bc, Chen Xiang-Wei (陈向炜)d
a Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; b Department of Mechanics, Shanghai University, Shanghai 200072, China; c Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, Chinad Shangqiu Teachers College, Shangqiu 476000, China
Abstract This paper investigates the momentum-dependent symmetries for nonholonomic nonconservative Hamilton canonical systems. The definition and determining equations of the momentum-dependent symmetries are presented, based on the invariance of differential equations under infinitesimal transformations with respect to the generalized coordinates and generalized momentums. The structure equation and the non-Noether conserved quantities of the systems are obtained. The inverse issues associated with the momentum-dependent symmetries are discussed. Finally, an example is discussed to further illustrate the applications.
Received: 06 December 2004
Revised: 06 December 2005
Accepted manuscript online:
PACS:
45.05.+x
(General theory of classical mechanics of discrete systems)
(General properties, structure, and representation of Lie groups)
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10372053) and the Natural Science Foundation of Henan Province, China (Grant Nos 0311011400 and 0511022200) and the State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences.
Cite this article:
Fu Jing-Li (傅景礼), Chen Li-Qun (陈立群), Chen Xiang-Wei (陈向炜) Momentum-dependent symmetries and non-Noether conserved quantities for nonholonomic nonconservative Hamilton canonical systems 2006 Chinese Physics 15 8
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