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)
a College of Physics Science and Technology, China University of Petroleum, Dongying 257061, China; b Department of Physics, Hexi University, Zhangye 734000, China
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.
Received: 30 October 2005
Revised: 14 March 2006
Accepted manuscript online:
Fang Jian-Hui(方建会), Liao Yong-Pan(廖永潘), Ding Ning(丁宁), and Wang Peng(王鹏) Noether--Lie symmetry and conserved quantities of mechanical system in phase space 2006 Chinese Physics 15 2792
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