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For a holonomic system in relative motion, the conformal invariance and the conserved quantity of Mei symmetry with Appell equations are investigated. First, by using the infinitesimal one-parameter transformation group and the infinitesimal generator vector, the definitions of Mei symmetry and the conformal invariance with Appell equations in a holonomic system in relative motion are given, and the determining equations of the conformal invariance of Mei symmetry for the system are derived. Relationship between the conformal invariance and Mei symmetry for the system is mainly studied. Then, by means of the structural equation which the gauge function satisfies, the expression of Mei conserved quantity deduced from Mei symmetry for the system is obtained. Finally, an example is given to illustrate the application of the result.
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Keywords:
- relative motion /
- holonomic system /
- Appell equation /
- conformal invariance
[1] Jia L Q, Wang X X, Zhang M L, Han Y L 2012 Nonlinear Dyn. 69 1807
[2] Han Y L, Wang X X, Zhang, M L, Jia L Q 2013 Nonlinear Dyn. 71 401
[3] Jia L Q, Sun X T, Zhang M L, Zhang Y Y, Han Y L 2014 Acta Phys. Sin. 63 010201 (in Chinese) [贾利群, 孙现亭, 张美玲, 张耀宇, 韩月林 2014 63 010201]
[4] Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Acta Phys. Sin. 62 110201 (in Chinese) [韩月林, 王肖肖, 张美玲, 贾利群 2013 62 110201]
[5] Chen X W, Li Y M, Zhao Y H 2005 Phys. Lett. A 337 274
[6] Luo S K, Li L 2013 Nonlinear Dyn. 73 639
[7] Luo S K, Li L 2013 Nonlinear Dyn. 73 339
[8] Luo S K, Li Z J, Peng W, Li L 2013 Acta Mech. 224 71
[9] Luo S K, Li Z J, Li L 2012 Acta Mech. 223 2621
[10] Jiang W A, Luo S K 2012 Nonlinear Dyn. 67 475
[11] Wang X X, Han YL, Zhang M L, Jia L Q 2013 Chin. Phys. B 22 020201
[12] Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 73 357
[13] Han Y L, Wang X X, Zhang M L, Jia L Q 2014 Journal of Mechanics. 30 21
[14] Wang P, Fang J H, Wang X M 2009 Chin. Phys. B 18 1312
[15] Fang J H 2010 Chin. Phys. B 19 040301
[16] Cui J C, Han Y L, Jia L Q 2012 Chin. Phys. B 21 080201
[17] Jia L Q, Xie Y L, Zhang Y Y, Yang X F 2010 Chin. Phys. B 19 110301
[18] Jia L Q, Zhang M L, Wang X X, Han Y L 2012 Chin. Phys. B 21 070204
[19] Wang X X, Sun X T, Zhang M L, Xie Y L, Jia L Q 2011 Chin. Phys. B 20 124501
[20] Fang J H, Zhang B, Zhang W W, Xu R L 2012 Chin. Phys. B 21 050202
[21] Zhang B, Fang J H, Zhang W W 2012 Chin. Phys. B 21 070208
[22] Xia L L, Cai J L 2010 Chin. Phys. B 19 040302
[23] Cai J L, Shi S S, Fang H J, Xu J 2012 Meccanica. 47 63
[24] Huang W L, Cai J L 2012 Acta Mech. 223 433
[25] Cai J L 2012 Nonlinear Dyn. 69 487
[26] Han Y L, Sun X T, Zhang Y Y, Jia L Q 2013 Acta Phys. Sin. 62 160201 (in Chinese) [韩月林, 孙现亭, 张耀宇, 贾利群 2013 62 160201]
[27] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems( Beijing: Science Press) (in Chinese) [梅凤翔 1999 李群和李代数对约束力学系统的应用(北京: 科学学出版社)]
[28] 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)]
[29] Zhang M L, Wang X X, Han Y L, Jia L Q 2012 Journal of Yunnan University (Natural Sciences Edition) 34 664 (in Chinese) [张美玲, 王肖肖, 韩月林, 贾利群 2012 云南大学学报 34 664]
[30] Chen X W, Zhao Y H, Li Y M 2009 Chin. Phys. B 18 3139
[31] Zhang M L, Wang X X, Han Y L, Jia L Q 2012 Chin. Phys. B 21 100203
[32] Xie Y L, Jia L Q, Luo S K 2011 Chin. Phys. B 20 010203
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[1] Jia L Q, Wang X X, Zhang M L, Han Y L 2012 Nonlinear Dyn. 69 1807
[2] Han Y L, Wang X X, Zhang, M L, Jia L Q 2013 Nonlinear Dyn. 71 401
[3] Jia L Q, Sun X T, Zhang M L, Zhang Y Y, Han Y L 2014 Acta Phys. Sin. 63 010201 (in Chinese) [贾利群, 孙现亭, 张美玲, 张耀宇, 韩月林 2014 63 010201]
[4] Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Acta Phys. Sin. 62 110201 (in Chinese) [韩月林, 王肖肖, 张美玲, 贾利群 2013 62 110201]
[5] Chen X W, Li Y M, Zhao Y H 2005 Phys. Lett. A 337 274
[6] Luo S K, Li L 2013 Nonlinear Dyn. 73 639
[7] Luo S K, Li L 2013 Nonlinear Dyn. 73 339
[8] Luo S K, Li Z J, Peng W, Li L 2013 Acta Mech. 224 71
[9] Luo S K, Li Z J, Li L 2012 Acta Mech. 223 2621
[10] Jiang W A, Luo S K 2012 Nonlinear Dyn. 67 475
[11] Wang X X, Han YL, Zhang M L, Jia L Q 2013 Chin. Phys. B 22 020201
[12] Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 73 357
[13] Han Y L, Wang X X, Zhang M L, Jia L Q 2014 Journal of Mechanics. 30 21
[14] Wang P, Fang J H, Wang X M 2009 Chin. Phys. B 18 1312
[15] Fang J H 2010 Chin. Phys. B 19 040301
[16] Cui J C, Han Y L, Jia L Q 2012 Chin. Phys. B 21 080201
[17] Jia L Q, Xie Y L, Zhang Y Y, Yang X F 2010 Chin. Phys. B 19 110301
[18] Jia L Q, Zhang M L, Wang X X, Han Y L 2012 Chin. Phys. B 21 070204
[19] Wang X X, Sun X T, Zhang M L, Xie Y L, Jia L Q 2011 Chin. Phys. B 20 124501
[20] Fang J H, Zhang B, Zhang W W, Xu R L 2012 Chin. Phys. B 21 050202
[21] Zhang B, Fang J H, Zhang W W 2012 Chin. Phys. B 21 070208
[22] Xia L L, Cai J L 2010 Chin. Phys. B 19 040302
[23] Cai J L, Shi S S, Fang H J, Xu J 2012 Meccanica. 47 63
[24] Huang W L, Cai J L 2012 Acta Mech. 223 433
[25] Cai J L 2012 Nonlinear Dyn. 69 487
[26] Han Y L, Sun X T, Zhang Y Y, Jia L Q 2013 Acta Phys. Sin. 62 160201 (in Chinese) [韩月林, 孙现亭, 张耀宇, 贾利群 2013 62 160201]
[27] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems( Beijing: Science Press) (in Chinese) [梅凤翔 1999 李群和李代数对约束力学系统的应用(北京: 科学学出版社)]
[28] 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)]
[29] Zhang M L, Wang X X, Han Y L, Jia L Q 2012 Journal of Yunnan University (Natural Sciences Edition) 34 664 (in Chinese) [张美玲, 王肖肖, 韩月林, 贾利群 2012 云南大学学报 34 664]
[30] Chen X W, Zhao Y H, Li Y M 2009 Chin. Phys. B 18 3139
[31] Zhang M L, Wang X X, Han Y L, Jia L Q 2012 Chin. Phys. B 21 100203
[32] Xie Y L, Jia L Q, Luo S K 2011 Chin. Phys. B 20 010203
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