Lie–Mei symmetry and conserved quantities of the Rosenberg problem

doi:10.1088/1674-1056/20/7/070204

中国物理B ›› 2011, Vol. 20 ›› Issue (7): 70204-070204.doi: 10.1088/1674-1056/20/7/070204

Lie–Mei symmetry and conserved quantities of the Rosenberg problem

刘晓巍, 李元成

College of Physics Science and Technology, China University of Petroleum (East China), Qingdao 266555, China

收稿日期:2010-11-26 修回日期:2011-01-27 出版日期:2011-07-15 发布日期:2011-07-15

Lie–Mei symmetry and conserved quantities of the Rosenberg problem

Liu Xiao-Wei(刘晓巍) and Li Yuan-Cheng(李元成)^†

College of Physics Science and Technology, China University of Petroleum (East China), Qingdao 266555, China

Received:2010-11-26 Revised:2011-01-27 Online:2011-07-15 Published:2011-07-15

摘要/Abstract

摘要： The Rosenberg problem is a typical but not too complicated problem of nonholonomic mechanical systems. The Lie—Mei symmetry and the conserved quantities of the Rosenberg problem are studied. For the Rosenberg problem, the Lie and the Mei symmetries for the equation are obtained, the conserved quantities are deduced from them and then the definition and the criterion for the Lie—Mei symmetry of the Rosenberg problem are derived. Finally, the Hojman conserved quantity and the Mei conserved quantity are deduced from the Lie—Mei symmetry.

Abstract: The Rosenberg problem is a typical but not too complicated problem of nonholonomic mechanical systems. The Lie—Mei symmetry and the conserved quantities of the Rosenberg problem are studied. For the Rosenberg problem, the Lie and the Mei symmetries for the equation are obtained, the conserved quantities are deduced from them and then the definition and the criterion for the Lie—Mei symmetry of the Rosenberg problem are derived. Finally, the Hojman conserved quantity and the Mei conserved quantity are deduced from the Lie—Mei symmetry.

Key words: nonholonomic systems, Rosenberg problem, Lie—Mei symmetry, 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. Lie–Mei symmetry and conserved quantities of the Rosenberg problem[J]. 中国物理B, 2011, 20(7): 70204-070204.

Liu Xiao-Wei(刘晓巍) and Li Yuan-Cheng(李元成). Lie–Mei symmetry and conserved quantities of the Rosenberg problem[J]. Chin. Phys. B, 2011, 20(7): 70204-070204.

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Lie–Mei symmetry and conserved quantities of the Rosenberg problem

Lie–Mei symmetry and conserved quantities of the Rosenberg problem

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