Noether symmetries of discrete mechanico-electrical systems

doi:10.1088/1674-1056/17/12/003

中国物理B ›› 2008, Vol. 17 ›› Issue (12): 4354-4360.doi: 10.1088/1674-1056/17/12/003

Noether symmetries of discrete mechanico-electrical systems

谢凤萍¹, 傅景礼², 陈本永³

(1)Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; (2)Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; (3)Institute of Mechanical and Automatism Controlcal Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, China

收稿日期:2008-03-06 修回日期:2008-08-29 出版日期:2008-12-20 发布日期:2008-12-20
基金资助:
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).

Noether symmetries of discrete mechanico-electrical systems

Fu Jing-Li (傅景礼)^a, Chen Ben-Yong(陈本永)^b, Xie Feng-Ping (谢凤萍)^a

^a Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; ^b Institute of Mechanical and Automatism Controlcal Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, China

Received:2008-03-06 Revised:2008-08-29 Online:2008-12-20 Published:2008-12-20
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: Noether symmetry, conservation law, discrete mechanico-electrical system, dissipative function

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.

Key words: Noether symmetry, conservation law, discrete mechanico-electrical system, dissipative function

中图分类号: (General theory of classical mechanics of discrete systems)

45.05.+x

02.20.Qs (General properties, structure, and representation of Lie groups) 02.30.Jr (Partial differential equations)

傅景礼, 陈本永, 谢凤萍. Noether symmetries of discrete mechanico-electrical systems[J]. 中国物理B, 2008, 17(12): 4354-4360.

Fu Jing-Li (傅景礼), Chen Ben-Yong(陈本永), Xie Feng-Ping (谢凤萍). Noether symmetries of discrete mechanico-electrical systems[J]. Chin. Phys. B, 2008, 17(12): 4354-4360.

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Noether symmetries of discrete mechanico-electrical systems

Noether symmetries of discrete mechanico-electrical systems

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