中国物理B ›› 2006, Vol. 15 ›› Issue (12): 2792-2795.doi: 10.1088/1009-1963/15/12/005

• GENERAL • 上一篇    下一篇

Noether--Lie symmetry and conserved quantities of mechanical system in phase space

方建会1, 丁 宁1, 王 鹏1, 廖永潘2   

  1. (1)College of Physics Science and Technology, China University of Petroleum, Dongying 257061, China; (2)Department of Physics, Hexi University, Zhangye 734000, China
  • 收稿日期:2005-10-30 修回日期:2006-03-14 出版日期:2006-12-20 发布日期:2006-12-20

Noether--Lie symmetry and conserved quantities of mechanical system in phase space

Fang Jian-Hui(方建会)a), Liao Yong-Pan(廖永潘)b), Ding Ning(丁宁)a), and Wang Peng(王鹏)a)   

  1. a College of Physics Science and Technology, China University of Petroleum, Dongying 257061, China; b Department of Physics, Hexi University, Zhangye 734000, China
  • Received:2005-10-30 Revised:2006-03-14 Online:2006-12-20 Published:2006-12-20

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摘要： In this paper, a new kind of symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e. a Noether--Lie symmetry, is presented, and the criterion of this symmetry is also given. The Noether conserved quantity and the generalized Hojman conserved quantity of the Noether--Lie symmetry of the system are obtained. The Noether--Lie symmetry contains the Noether symmetry and the Lie symmetry, and has more generalized significance.

Abstract: In this paper, a new kind of symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e. a Noether--Lie symmetry, is presented, and the criterion of this symmetry is also given. The Noether conserved quantity and the generalized Hojman conserved quantity of the Noether--Lie symmetry of the system are obtained. The Noether--Lie symmetry contains the Noether symmetry and the Lie symmetry, and has more generalized significance.

Key words: Noether--Lie symmetry, mechanical system, conserved quantity, phase space

中图分类号:  (Lagrangian and Hamiltonian mechanics)

  • 45.20.Jj
02.30.Jr (Partial differential equations)