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In this paper, the conformal invariance and Mei symmetry for a generalized Hamilton system under infinitesimal transformations are discussed in details. A necessary and sufficient condition for conformal invariance of systems to be Mei symmetry is given. We get the Mei conserved quantities of the conformal invariance. Finally, an example is given to illustrate the application of the result.
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Keywords:
- generalized Hamilton system /
- conformal invariance /
- Mei symmetry
[1] Noether A E 1918 Nachr. Akad. Wiss. Gottingen: Math. Phys. 2 235
[2] Lutzky M 1979 J. Phys A: Math Gen. 12 973
[3] Mei F X 2000 J. Beijing Inst. Technol. 9 120
[4] Fang J H 2003 Commun. Theor. Phys. 40 269
[5] Luo S K 2003 Acta Phys. Sin. 52 2941 (in Chinese) [罗绍凯 2003 物理学报 52 2941]
[6] Mei F X 2003 Acta Phys. Sin. 52 1048 (in Chinese) [梅凤翔 2003 物理学报 52 1048]
[7] Liu C, Liu S X, Mei F X, Guo Y X 2008 Acta Phys. Sin. 57 6709 (in Chinese) [刘畅, 刘世兴, 梅凤翔, 郭永新 2008 物理学报 57 6709]
[8] Wu H B 2004 Tran. of Beijing Inst. of Technol. 24 20 (in Chinese) [吴慧彬 2004 北京理工大学学报 24 20]
[9] Jia L Q, Zheng S W 2006 Acta Phys. Sin. 55 3829 (in Chinese) [贾利群, 郑世旺 2006 物理学报 55 3829]
[10] Jiang W A, Luo S K 2011 Acta Phys. Sin. 60 060201 (in Chinese) [姜文安, 罗绍凯 2011 物理学报 60 060201]
[11] Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 2004 约束力学系统的对称性与守恒量(北京: 北京理工大学出版社)]
[12] Guo X Y, Liu H W, Xu Z H 2013 Journal of Northeast Dianli University 33 162 (in Chinese) [郭秀英, 刘洪伟, 徐中海 2013 东北电力大学学报 33 162]
[13] Fang J H, Ding N, Wang P 2007 Chin. Phys. 16 887
[14] Cui J C, Zhang Y Y, Jia L Q 2009 Chin. Phys. B 18 1731
[15] Jia L Q, Xie Y L, Zhang Y Y, Yang X F 2010 Chin. Phys. B 19 110301
[16] Robert M L, Matthew P 2001 J. Geom. Phys. 39 276
[17] Luo S K, Li Z J, Peng W, Li L 2013 Acta Mech. 224 71
[18] Luo S K, Li L 2013 Nonlinear Dyn. 73 339
[19] Jiang W A, Luo S K 2012 Nonlinear Dyn. 67 475
[20] Luo S K, Li L 2013 Nonlinear Dyn. 73 639
[21] Li L, Peng W, Xu Y L, Luo S K 2013 Nonlinear Dyn. 72 663
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[1] Noether A E 1918 Nachr. Akad. Wiss. Gottingen: Math. Phys. 2 235
[2] Lutzky M 1979 J. Phys A: Math Gen. 12 973
[3] Mei F X 2000 J. Beijing Inst. Technol. 9 120
[4] Fang J H 2003 Commun. Theor. Phys. 40 269
[5] Luo S K 2003 Acta Phys. Sin. 52 2941 (in Chinese) [罗绍凯 2003 物理学报 52 2941]
[6] Mei F X 2003 Acta Phys. Sin. 52 1048 (in Chinese) [梅凤翔 2003 物理学报 52 1048]
[7] Liu C, Liu S X, Mei F X, Guo Y X 2008 Acta Phys. Sin. 57 6709 (in Chinese) [刘畅, 刘世兴, 梅凤翔, 郭永新 2008 物理学报 57 6709]
[8] Wu H B 2004 Tran. of Beijing Inst. of Technol. 24 20 (in Chinese) [吴慧彬 2004 北京理工大学学报 24 20]
[9] Jia L Q, Zheng S W 2006 Acta Phys. Sin. 55 3829 (in Chinese) [贾利群, 郑世旺 2006 物理学报 55 3829]
[10] Jiang W A, Luo S K 2011 Acta Phys. Sin. 60 060201 (in Chinese) [姜文安, 罗绍凯 2011 物理学报 60 060201]
[11] Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 2004 约束力学系统的对称性与守恒量(北京: 北京理工大学出版社)]
[12] Guo X Y, Liu H W, Xu Z H 2013 Journal of Northeast Dianli University 33 162 (in Chinese) [郭秀英, 刘洪伟, 徐中海 2013 东北电力大学学报 33 162]
[13] Fang J H, Ding N, Wang P 2007 Chin. Phys. 16 887
[14] Cui J C, Zhang Y Y, Jia L Q 2009 Chin. Phys. B 18 1731
[15] Jia L Q, Xie Y L, Zhang Y Y, Yang X F 2010 Chin. Phys. B 19 110301
[16] Robert M L, Matthew P 2001 J. Geom. Phys. 39 276
[17] Luo S K, Li Z J, Peng W, Li L 2013 Acta Mech. 224 71
[18] Luo S K, Li L 2013 Nonlinear Dyn. 73 339
[19] Jiang W A, Luo S K 2012 Nonlinear Dyn. 67 475
[20] Luo S K, Li L 2013 Nonlinear Dyn. 73 639
[21] Li L, Peng W, Xu Y L, Luo S K 2013 Nonlinear Dyn. 72 663
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