The approximate conserved quantity of the weakly nonholonomic mechanical-electrical system

doi:10.1088/1674-1056/20/7/070203

中国物理B ›› 2011, Vol. 20 ›› Issue (7): 70203-070203.doi: 10.1088/1674-1056/20/7/070203

The approximate conserved quantity of the weakly nonholonomic mechanical-electrical system

刘晓巍¹, 李元成¹, 夏丽莉²

(1)College of Physics Science and Technology, China University of Petroleum, Qingdao 266555, China; (2)Department of Physics, Henan Institute of Education, Zhengzhou 450014, China

收稿日期:2010-11-20 修回日期:2011-03-24 出版日期:2011-07-15 发布日期:2011-07-15

The approximate conserved quantity of the weakly nonholonomic mechanical-electrical system

Liu Xiao-Wei(刘晓巍)^a), Li Yuan-Cheng(李元成)^a)^†, and Xia Li-Li(夏丽莉)^b)

^a College of Physics Science and Technology, China University of Petroleum, Qingdao 266555, China; ^b Department of Physics, Henan Institute of Education, Zhengzhou 450014, China

Received:2010-11-20 Revised:2011-03-24 Online:2011-07-15 Published:2011-07-15

摘要/Abstract

摘要： We study the approximate conserved quantity of the weakly nonholonomic mechanical-electrical system. By means of the Lagrange—Maxwell equation, the Noether equality of the weakly nonholonomic mechanical-electrical system is obtained. The multiple powers-series expansion of the parameter of the generators of infinitesimal transformations and the gauge function is put into a generalized Noether identity. Using the Noether theorem, we obtain an approximate conserved quantity. An example is provided to prove the existence of the approximate conserved quantity.

Abstract: We study the approximate conserved quantity of the weakly nonholonomic mechanical-electrical system. By means of the Lagrange—Maxwell equation, the Noether equality of the weakly nonholonomic mechanical-electrical system is obtained. The multiple powers-series expansion of the parameter of the generators of infinitesimal transformations and the gauge function is put into a generalized Noether identity. Using the Noether theorem, we obtain an approximate conserved quantity. An example is provided to prove the existence of the approximate conserved quantity.

Key words: weakly nonholonomic mechanical-electrical system, Noether theorem, approximate conserved quantity

中图分类号: (Lie algebras of Lie groups)

02.20.Sv

11.30.-j (Symmetry and conservation laws) 45.20.Jj (Lagrangian and Hamiltonian mechanics)

刘晓巍, 李元成, 夏丽莉. The approximate conserved quantity of the weakly nonholonomic mechanical-electrical system[J]. 中国物理B, 2011, 20(7): 70203-070203.

Liu Xiao-Wei(刘晓巍), Li Yuan-Cheng(李元成), and Xia Li-Li(夏丽莉) . The approximate conserved quantity of the weakly nonholonomic mechanical-electrical system[J]. Chin. Phys. B, 2011, 20(7): 70203-070203.

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The approximate conserved quantity of the weakly nonholonomic mechanical-electrical system

The approximate conserved quantity of the weakly nonholonomic mechanical-electrical system

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