THE PHYSICS OF ELEMENTARY PARTICLES AND FIELDS |
Prev
Next
|
|
|
Noether's theory of Lagrange systems in discrete case |
Lü Hong-Sheng(吕洪升)a), Zhang Hong-Bin(张宏彬)b)†, and Gu Shu-Long(顾书龙)b) |
a Department of Mathematics, Chaohu University, Chaohu 238000, China; b Department of Physics , Chaohu University, Chaohu 238000, China |
|
|
Abstract In this paper, Noether theory of Lagrange systems in discrete case are studied. First, we briefly overview the well-known Noether theory of Lagrange system in the continuous case. Then, we introduce some definitions and notations, such as the operators of discrete translation to the right and the left and the operators of discrete differentiation to the right and the left, and give the conditions for the invariance of the difference functional on the uniform lattice and the non-uniform one, respectively. We also deduce the discrete analog of the Noether-type identity. Finally, the discrete analog of Noether's theorem is presented. An example was discussed to illustrate these results.
|
Received: 28 February 2010
Revised: 01 July 2010
Accepted manuscript online:
|
PACS:
|
11.30.-j
|
(Symmetry and conservation laws)
|
|
45.20.Jj
|
(Lagrangian and Hamiltonian mechanics)
|
|
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10872037) and the Natural Science Foundation of Anhui Province, China (Grant No. 070416226). |
Cite this article:
Lü Hong-Sheng(吕洪升), Zhang Hong-Bin(张宏彬), and Gu Shu-Long(顾书龙) Noether's theory of Lagrange systems in discrete case 2011 Chin. Phys. B 20 011101
|
[1] |
Noether A E 1918 Nachr . Akad. Wiss. Gottingen Math. Phys. KI II 235
|
[2] |
Li Z P 1981 Acta Phys. Sin. 30 1659 (in Chinese)
|
[3] |
Mei F X 1999 Applications of Lie Group and Lie Algebra to Constrained Mechanical Systems (Beijing: Science Press) (in Chinese)
|
[4] |
Zhao Y Y and Mei F X 1999 The Symmetry and Invariant and of Mechanical Systems (Beijing: Science Press) (in Chinese)
|
[5] |
Fu J L and Chen L Q 2003 Phys. Lett. A 317 255
|
[6] |
Fu J L and Chen L Q 2004 Mech. Res. Commun. 31 9
|
[7] |
Chen X W, Li Y M and Zhao Y H 2005 Phys. Lett. A 337 274
|
[8] |
Liu R W and Chen L Q 2004 Chin. Phys. 13 1615
|
[9] |
Zhang H B and Chen L Q 2005 J. Phys. Soc. Jap. 74 905
|
[10] |
Zhang Y and Mei F X 2000 Chin. Sci. Bull. 45 1354
|
[11] |
Luo S K 2002 Chin. Phys. Lett. 19 449
|
[12] |
Guo Y X, Wang Y, Chen G Y and Mei F X 2005 J. Math. Phys. 46 062902
|
[13] |
Guo Y X, Liu S X, Liu C, Luo S K and Wang Y 2007 J. Math. Phys. 48 082901
|
[14] |
Wang S Y and Mei F X 2002 Chin. Phys. 11 5
|
[15] |
Wu H B 2005 Chin. Phys. 14 452
|
[16] |
Xu X J, Qin M C and Mei F X 2004 Acta Mech. Sin. 20 668
|
[17] |
Fang J H, Liao Y P, Ding N and Wang P 2006 Chin. Phys. 15 2792
|
[18] |
Li Y C, Jing H X, Xia L L, Wang J and Hou Q B 2007 Chin. Phys. 16 2154
|
[19] |
Ge W K and Mei F X 2007 Acta Phys. Sin. 56 2479 (in Chinese)
|
[20] |
Lou Z M 2007 Acta Phys. Sin. 56 2475 (in Chinese)
|
[21] |
Ge W K and Mei F X 2009 Acta Phys. Sin. 58 699 (in Chinese)
|
[22] |
Liu C , Zhao Y H and Chen X W 2010 Acta Phys. Sin. 59 11 (in Chinese)
|
[23] |
Gu S L and Zhang H B 2010 Acta Phys. Sin. 59 716 (in Chinese)
|
[24] |
Levi D and Winternitz P 1991 Phys. Lett. A 152 335
|
[25] |
Levi D and Winternitz P 1993 J. Math. Phys. 34 3713
|
[26] |
Levi D and Winternitz P 1996 J. Math. Phys. 37 5551
|
[27] |
Levi D and Rodriguez M A 1999 J. Phys. A: Math. Gen. 32 8303
|
[28] |
Levi D, Tremblay S and Winternitz P 2000 J. Phys. A: Math. Gen. 33 8507
|
[29] |
Hydon P E 2000 Proc. R. Soc. A 456 2835
|
[30] |
Levi D and Winternitz P 2006 J. Phys. A: Math.Gen. 36 R1
|
[31] |
Dorodnitsyn V A 1991 J. Sov. Math. 55 1490
|
[32] |
Dorodnitsyn V A 1998 Int. J. Mod. Phys. 5 723
|
[33] |
Dorodnitsyn V A and Winternitz P 2000 Nonlinear Dynamics 22 49
|
[34] |
Dorodnitsyn V A, Kozlov R and Winternitz P 2000 J. Math. Phys. 41 480
|
[35] |
Dorodnitsyn V A and Kozlov R 2003 J. Nonl. Math. Phys. 10 16
|
[36] |
Dorodnitsyn V A, Kozlov R and Winternitz P 2004 J. Math. Phys. 45 336
|
[37] |
Zhang H B, Chen L Q and Liu R W 2005 Chin. Phys. 14 1063
|
[38] |
Fu J L, Dai G D, Jim'enez S and Tang Y F 2007 Chin. Phys. 16 570
|
[39] |
Dorodnitsyn V A 2001 Appl. Numer. Math. 307 321
|
[40] |
Fu J L, Chen L Q and Chen B Y 2009 Sin. China Ser. G 39 1320 endfootnotesize
|
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|