ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS |
Prev
Next
|
|
|
Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems |
Chen Rong (陈蓉), Xu Xue-Jun (许学军) |
Department of Physics, Zhejiang Normal University, Jinhua 321004, China |
|
|
Abstract In this paper, the relation of the conformal invariance, the Noether symmetry, and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is given. The relation between the conformal invariance and the Noether symmetry is discussed, the conformal factors of the determining expressions are found by using the Noether symmetry, and the Noether conserved quantity resulted from the conformal invariance is obtained. The relation between the conformal invariance and the Lie symmetry is discussed, the conformal factors are found by using the Lie symmetry, and the Hojman conserved quantity resulted from the conformal invariance of the system is obtained. Two examples are given to illustrate the application of the results.
|
Received: 14 December 2011
Revised: 31 May 2012
Accepted manuscript online:
|
PACS:
|
11.30.-j
|
(Symmetry and conservation laws)
|
|
45.20.Jj
|
(Lagrangian and Hamiltonian mechanics)
|
|
02.20.Sv
|
(Lie algebras of Lie groups)
|
|
Corresponding Authors:
Xu Xue-Jun
E-mail: xxj@zjnu.cn
|
Cite this article:
Chen Rong (陈蓉), Xu Xue-Jun (许学军) Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems 2012 Chin. Phys. B 21 094501
|
[1] |
Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese)
|
[2] |
Mei F X and Liu Y 1991 Advanced Analytical Mechanics (Beijing: Beijing Institute of Technology Press) (in Chinese)
|
[3] |
Noether A E 1918 Nachr. Akad. Wiss. Göttingen. Math. Phys. KI II 235
|
[4] |
Galiullin A S, Gafarov G G and Malaishka R P 1997 Analytical Dynamics of Helmholtz Birkhoff and Nambu Systems (Moscow: UFN) (in Russian)
|
[5] |
Cai J L and Mei F X 2008 Acta Phys. Sin. 57 5369 (in Chinese)
|
[6] |
Liu C, Mei F X and Guo Y X 2008 Acta Phys. Sin. 57 6704 (in Chinese)
|
[7] |
Chen X W, Zhao Y H and Liu C 2009 Acta Phys. Sin. 58 5150 (in Chinese)
|
[8] |
Chen X W, Liu C and Mei F X 2008 Chin. Phys. B 17 3180
|
[9] |
Cai J L, Luo S K and Mei F X 2008 Chin. Phys. B 17 3170
|
[10] |
Cai J L 2008 Chin. Phys. Lett. 25 1523
|
[11] |
Fu J L, Wang X J and Xie F P 2008 Chin. Phys. Lett. 25 2413
|
[12] |
Liu C, Mei F X and Guo Y X 2009 Chin. Phys. B 18 395
|
[13] |
Liu C, Liu S X, Mei F X and Guo Y X 2009 Chin. Phys. B 18 0856
|
[14] |
Zhang Y 2009 Chin. Phys. B 18 4636
|
[15] |
Li Y C, Xia L L and Wang X M 2009 Chin. Phys. B 18 4643
|
[16] |
Zhang M J, Fang J H, Lu K, Zhang K J and Li Y 2009 Chin. Phys. B 18 4650
|
[17] |
Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese)
|
[18] |
Xia L L and Cai J L 2010 Chin. Phys. B 19 040302
|
[19] |
Luo Y P and Fu J L 2010 Chin. Phys. B 19 090303
|
[20] |
Li Y M 2010 Journal of Yunnan University 32 52 (in Chinese)
|
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
|
|
|