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

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

中国物理B ›› 2010, Vol. 19 ›› Issue (4): 40301-040301.doi: 10.1088/1674-1056/19/4/040301

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

方建会

College of Physics Science and Technology, China University of Petroleum, Dongying 257061, China

收稿日期:2009-02-15 修回日期:2009-08-26 出版日期:2010-04-15 发布日期:2010-04-15

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

Fang Jian-Hui(方建会)^†

College of Physics Science and Technology, China University of Petroleum, Dongying 257061, China

Received:2009-02-15 Revised:2009-08-26 Online:2010-04-15 Published:2010-04-15

摘要/Abstract

摘要： 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.

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.

Key words: Lagrange system, Lie symmetry, new conserved quantity

中图分类号: (Lagrangian and Hamiltonian mechanics)

45.20.Jj

02.20.Sv (Lie algebras of Lie groups)

方建会. A new type of conserved quantity of Lie symmetry for the Lagrange system[J]. 中国物理B, 2010, 19(4): 40301-040301.

Fang Jian-Hui(方建会). A new type of conserved quantity of Lie symmetry for the Lagrange system[J]. Chin. Phys. B, 2010, 19(4): 40301-040301.

参考文献 22

[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)

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

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

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