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Chin. Phys. B, 2008, Vol. 17(12): 4354-4360    DOI: 10.1088/1674-1056/17/12/003
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Noether symmetries of discrete mechanico-electrical systems

Xie Feng-Pinga, Fu Jing-Lib, Chen Ben-Yongc
a Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; b Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; c Institute of Mechanical and Automatism Controlcal Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, China
Abstract  This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electrical systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of varitional principle, the discrete analogue of Lagrange-Maxwell equations, the discrete analogue of Noether theorems for Lagrange-Maxwell and Lagrange machanico-electrical systems. Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results.
Keywords:  dissipative function      Noether symmetry      conservation law      discrete mechanico-electrical system     
Received:  06 March 2008      Published:  20 December 2008
PACS:  45.05.+x (General theory of classical mechanics of discrete systems)  
  02.20.Qs (General properties, structure, and representation of Lie groups)  
  02.30.Jr (Partial differential equations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos 10672143 and 60575055) and the Natural Science Foundation of Henan Province, China (Grant No 0511022200).

Cite this article: 

Xie Feng-Ping, Fu Jing-Li, Chen Ben-Yong Noether symmetries of discrete mechanico-electrical systems 2008 Chin. Phys. B 17 4354

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