Perturbation to Noether Symmetry and Noether adiabatic Invariants of Discrete Mechanico-Electrical Systems
WANG Peng
College of Physics and Electronic Engineering, Xinjiang Normal University, Urumqi 830054 Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072
Perturbation to Noether Symmetry and Noether adiabatic Invariants of Discrete Mechanico-Electrical Systems
WANG Peng
College of Physics and Electronic Engineering, Xinjiang Normal University, Urumqi 830054 Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072
摘要Perturbation to Noether symmetry of discrete mechanico-electrical systems on an uniform lattice is investigated. First, Noether theorem of a system is presented. Secondly, the criterion of perturbation to Noether symmetry of the system is given. Based on the definition of adiabatic invariants, Noether adiabatic invariants of the system are obtained. Finally, An example is given to support these results.
Abstract：Perturbation to Noether symmetry of discrete mechanico-electrical systems on an uniform lattice is investigated. First, Noether theorem of a system is presented. Secondly, the criterion of perturbation to Noether symmetry of the system is given. Based on the definition of adiabatic invariants, Noether adiabatic invariants of the system are obtained. Finally, An example is given to support these results.
(General theory of classical mechanics of discrete systems)
引用本文:
WANG Peng
. Perturbation to Noether Symmetry and Noether adiabatic Invariants of Discrete Mechanico-Electrical Systems[J]. 中国物理快报, 2011, 28(4): 40203-040203.
WANG Peng
. Perturbation to Noether Symmetry and Noether adiabatic Invariants of Discrete Mechanico-Electrical Systems. Chin. Phys. Lett., 2011, 28(4): 40203-040203.
[1] Bluman G W and Anco S C 2004 Symmetries and integration methods for Differential Equations (New York: Springer-Verlag)
[2] Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese)
[3] Guo Y X, Luo S K, Shang M and Mei F X 2001 Rep. Math. Phys. 47 313
[4] Jia L Q, Cui J C and Luo S K, Yang X F 2009 Chin. Phys. Lett. 26 030303
[5] Cai J L 2010 Int. J. Theor. Phys. 49 201
[6] Fang J H, Zhang M J and Zhang W W 2010 Phys. Lett. A 374 1801
[7] LeviD and Winternitz P 2006 J. Phys. A: Math. Theor. 39 R1
[8] Dorodnitsyn V A and Kozlov R V 2009 J. Phys. A: Math. Theor. 42 454007
[9] Zhang H B, Lv H S and Gu S L 2010 Acta Phys. Sin. 59 5213 (in Chinese)
[10] Fu J L, Chen B Y and Xie F P 2008 Chin. Phys. B 17 4354
[11] Zhao Y Y and Mei F X 1999 Symmetries and Invariants of Mechanical systems (Beijing: Science Press) (in Chinese)
[12] Kara A H and Mahomed F M 1999 Int. J. Theor. Phys. 38 2389
[13] Chen X W, Li Y M and Zhao Y H 2005 Phys. Lett. A 337 274
[14] Zhang Y, Fan C X and Mei F X 2006 Acta Phys. Sin. 55 3237 (in Chinese)
[15] Luo S K 2007 Acta Phys. Sin. 57 5580 (in Chinese).
[16] Wang P, Fang J H and Wang X M 2009 Chin. Phys. Lett. 26 034501
[17] Zhang M J, Fang J H, Lu K, Zhang K J and Li Y 2009 Chin. Phys. Lett. 26 120201
2011, Vol. 28 
