A new type of conserved quantity of Lie symmetry for the Lagrange system

doi:10.1088/1674-1056/19/4/040301

Abstract This paper studies a new type of conserved quantity which is directly induced by Lie symmetry of the Lagrange system. Firstly, the criterion of Lie symmetry for the Lagrange system is given. Secondly, the conditions of existence of the new conserved quantity as well as its forms are proposed. Lastly, an example is given to illustrate the application of the result.

Keywords: Lagrange system Lie symmetry new conserved quantity

Received: 15 February 2009
Revised: 26 August 2009
Accepted manuscript online:

PACS:	45.20.Jj	(Lagrangian and Hamiltonian mechanics)
	02.20.Sv	(Lie algebras of Lie groups)

Cite this article:

Fang Jian-Hui(方建会) A new type of conserved quantity of Lie symmetry for the Lagrange system 2010 Chin. Phys. B 19 040301

[1]	Noether A E 1918 Math. Phys. KI II 235
[2]	Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese)
[3]	Lutzky M 1979 J. Phys. A: Math. Gen. 12 973
[4]	Mei F X 2001 Chin. Phys. 10 177
[5]	Fang J H 2003 Commun. Theor. Phys. 40 269
[6]	Luo S K 2003 Acta Phys. Sin. 52 2941 (in Chinese)
[7]	Zhang Y 2005 Acta Phys. Sin. 54 2980 (in Chinese)
[8]	Guo Y X, Jiang L Y and Yu Y 2001 Chin. Phys. 10 181
[9]	Wang S Y and Mei F X 2002 Chin. Phys. 11 5
[10]	Mei F X, Xu X J and Zhang Y F 2004 Acta Mech. Sin. 20] 668
[11]	Wu H B 2004 Chin. Phys. 13 589
[12]	Zhang H B and Chen L Q 2005 J. Phys. Soc. Jpn. 74 905
[13]	Chen X W, Li Y M and Zhao Y H 2005 Phys. Lett. A 337 274
[14]	Xu X J, Qin M C and Mei F X 2005 Chin. Phys. 14 1287
[15]	Fu J L, Chen L Q, Jimenez S and Tang Y F 2006 Phys. Lett. A 358 5
[16]	Fang J H, Ding N and Wang P 2007 Acta Phys. Sin. 56 3039 (in Chinese)
[17]	Jia L Q, Zhang Y Y and Luo S K 2007 Chin. Phys. 16 3168
[18]	Lou Z M 2007 Acta Phys. Sin. 56 2475 (in Chinese)
[19]	Zheng S W, Xie J F and Chen W C 2008 Chin. Phys. Lett. 25 809
[20]	Shi S Y, Fu J L, Huang X H, Chen L Q and Zhang X B 2008 Chin. Phys. B 17 754
[21]	Cai J L and Mei F X 2008 Acta Phys. Sin. 57 5369 (in Chinese)
[22]	Huang X H, Zhang X B and Shi S Y 2008 Acta Phys. Sin. 57 6056 (in Chinese)

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