摘要Conformal invariance and conserved quantities for a higher-order Lagrange system by Lie point transformation of groups are studied. The differential equation of motion for the higher-order Lagrange system is introduced. The definition of conformal invariance for the system together with its determining equations and conformal factor are provided. The necessary and sufficient condition that the system's conformal invariance would be Lie symmetry by the infinitesimal one-parameter point transformation group is deduced. The conserved quantity of the system is derived using the structural equation satisfied by the gauge function. An example of a higher-order mechanical system is offered to illustrate the application of the result.
Abstract：Conformal invariance and conserved quantities for a higher-order Lagrange system by Lie point transformation of groups are studied. The differential equation of motion for the higher-order Lagrange system is introduced. The definition of conformal invariance for the system together with its determining equations and conformal factor are provided. The necessary and sufficient condition that the system's conformal invariance would be Lie symmetry by the infinitesimal one-parameter point transformation group is deduced. The conserved quantity of the system is derived using the structural equation satisfied by the gauge function. An example of a higher-order mechanical system is offered to illustrate the application of the result.
HUANG Wei-Li;CAI Jian-Le**
. Conformal Invariance of Higher-Order Lagrange Systems by Lie Point Transformation[J]. 中国物理快报, 2011, 28(11): 110203-110203.
HUANG Wei-Li, CAI Jian-Le**
. Conformal Invariance of Higher-Order Lagrange Systems by Lie Point Transformation. Chin. Phys. Lett., 2011, 28(11): 110203-110203.
[1] Noether A E 1918 Nachr. Akad. Math. 2 235
[2] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science) (in Chinese)
[3] Zhao Y Y and Mei F X 1999 Symmetries and Invariants of Mechanical Systems (Beijing: Science) (in Chinese)
[4] Mei F X 2001 Chin. Phys. 10 177
[5] Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology) (in Chinese)
[6] Zhang Y 2005 Acta Phys. Sin. 54 2980 (in Chinese)
[7] Luo S K 2007 Chin. Phys. Lett. 24 3017
[8] Luo S K, Chen X W and Guo Y X 2007 Chin. Phys. 16 3176
[9] Luo S K and Zhang Y F et al 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing: Science) (in Chinese)
[10] Jia L Q, Cui J C, Luo S K and Yang X F 2009 Chin. Phys. Lett. 26 030303
[11] Fang J H, Zhang M J and Lu K 2009 Chin. Phys. Lett. 26 110202
[12] Zhang M J, Fang J H, Lu K and Zhang K J 2009 Chin. Phys. Lett. 26 120201
[13] LI Y M 2010 Chin. Phys. Lett. 27 010202
[14] Zheng S W, Xie J F, Wang J B and Chen X W 2010 Chin. Phys. Lett. 27 030307
[15] Xie Y L and Jia L Q 2010 Chin. Phys. Lett. 27 120201
[16] Jiang W A and Luo S K 2011 Acta Phys. Sin. 60 060201 (in Chinese)
[17] Li Z J, Jiang W A and Luo S K 2011 Nonlinear Dyn. (accepted)
[18] Jia L Q, Xie Y L and Luo S K 2011 Acta Phys. Sin. 60 040201 (in Chinese)
[19] Jiang W A, Li Z J and Luo S K 2011 Chin. Phys. B 20 030202
[20] Jiang W A and Luo S K 2011 Nonlinear Dyn. (accepted)
[21] Jiang W A, Li L, Li Z J and Luo S K 2011 Nonlinear Dyn. (accepted)
[22] Galiullin A S, Gafarov G G, Malaishka R P and Khwan A M 1997 Analytical Dynamics of Helmholtz, Birkhoff and Nambu Systems (Moscow: UFN) (in Russian)
[23] Cai J L and Mei F X 2008 Acta Phys. Sin. 57 5369 (in Chinese)
[24] Cai J L 2008 Chin. Phys. Lett. 25 1523
[25] Cai J L 2010 Int. J. Theor. Phys. 49 201
[26] Cai J L, Shi S S, Fang H J and Xu J 2011 Meccanica (accepted)
[27] He G and Mei F X 2008 Chin. Phys. B 17 2764
[28] Mei F X, Xie J F and Gang T Q 2008 Acta Mech. Sin. 24 583
[29] Xia L L, Cai J L and Li Y C 2009 Chin. Phys. B 18 3158
[30] Luo Y P 2009 Int. J. Theor. Phys. 48 2665
[31] Li Y C, Xia L L and Wang X M 2009 Chin. Phys. B 18 4643
[32] Zhang Y 2009 Chin. Phys. B 18 4636
[33] Luo Y P and Fu J L 2010 Chin. Phys. B 19 090303
[34] Cai J L 2009 Acta Phys. Pol. A 115 854
[35] Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese)
[36] Luo Y P and Fu J L 2010 Chin. Phys. B 19 090304
[37] Cai J L 2010 Acta Phys. Pol. A 117 445
[38] Luo Y P and Fu J L 2011 Chin. Phys. B 20 021102
[39] Zhang X W 2005 Acta Phys. Sin. 54 4483 (in Chinese)
2011, Vol. 28 
