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Chin. Phys., 2004, Vol. 13(11): 1784-1789    DOI: 10.1088/1009-1963/13/11/002
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Non-Noether symmetries and conserved quantities of the Lagrange mechano-electrical systems

Fu Jing-Lia, Chen Li-Qunb, Liu Rong-Wanc
a Department of Applied Physics, Zhejiang University of Science, Hangzhou 310018, China; Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; b Department of Mechanics, Shanghai University, Shanghai 200072, China; Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; c Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; Shaoguan University, Shaogua
Abstract  This paper focuses on studying non-Noether symmetries and conserved quantities of Lagrange mechano-electrical dynamical systems. Based on the relationships between the motion and Lagrangian, we present conservation laws on non-Noether symmetries for Lagrange mechano-electrical dynamical systems. A criterion is obtained on which non-Noether symmetry leads to Noether symmetry of the systems. The work also gives connections between the non-Noether symmetries and Lie point symmetries, and further obtains Lie invariants to form a complete set of non-Noether conserved quantity. Finally, an example is discussed to illustrate these results.
Keywords:  mechano-electrical system      infinitesimal transformation      non-Noether symmetry      non-Noether conserved quantity  
Received:  25 February 2004      Revised:  08 May 2004      Published:  20 June 2005
PACS:  02.20.Qs (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 (Grant No 0311011400).

Cite this article: 

Fu Jing-Li, Chen Li-Qun, Liu Rong-Wan Non-Noether symmetries and conserved quantities of the Lagrange mechano-electrical systems 2004 Chin. Phys. 13 1784

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