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For a holonomic system, the conformal invariance and conserved quantity of Mei symmetry for Appell equations are studied. Firstly, by the infinitesimal one-parameter transformation group and the infinitesimal generator vector, we define Mei symmetry and conformal invariance of differential equations of motion for holonomic system, and the determining equation of Mei symmetry and conformal invariance for holonomic system are given. Then, taking advantage of a structure equation that gauge function satisfies, the system corresponding Mei conserved quantity is derived. Finally, an example is given to illustrate the application of the result.
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Keywords:
- Appell equation /
- Mei symmetry /
- conformal invariance /
- Mei conserved quantity
[1] Lutzky M 1979 J. Phys. A Math. Gen. 12 973
[2] Noether A E 1918 Nachr. Akad. Math. 2 235
[3] 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)]
[4] Galiullin A S, Gafarov G G, Malaishka R P, Khwan A M 1997 Analytical Dynamics of Helmholtz, Birkhoff and Nambu Systems (Moscow: UFN) (in Russian)
[5] Zhang Y, Xue Y 2009 Chin. Q. Mech. 30 216 (in Chinese) [张毅, 薛纭2009力学季刊 30 216]
[6] Cai J L, Shi S S, Fang H J 2012 Meccanica 47 63
[7] Chen X W, Zhao Y H, Li Y M 2009 Chin. Phys. B 18 3139
[8] Cai J L, Shi S S 2012 Acta Phys. Sin. 61 030201 (in Chinese) [蔡建乐, 史生水2012 61 030201]
[9] Appell P 1953 Traité de Mécanique Rationnelle II (Paris: Gauthier-Villars) p335
[10] Xue W X 1987 Acta Mech. Sin. 19 156
[11] Luo S K 2002 Acta Phys. Sin. 51 712 (in Chinese) [罗绍凯2002 51 712]
[12] Cui J C, Zhang Y Y, Yang X F, Jia L Q 2010 Chin. Phys. B 19 030304
[13] Li Y C, Xia L L, Wang X M, Liu X W 2010 Acta Phys. Sin. 59 3639 (in Chinese) [李元成, 夏丽莉, 王小明, 刘晓巍2010 59 3639]
[14] Jia L Q, Xie Y L, Zhang Y Y, Cui J C, Yang X F 2010 Acta Phys. Sin. 59 7552 (in Chinese) [贾利群, 解银丽, 张耀宇, 崔金超, 杨新芳2010 59 7552]
[15] Yang X F, Sun X T, Wang X X, Zhang M L, Jia L Q 2011 Acta Phys. Sin. 60 111101 (in Chinese) [杨新芳, 孙现亭, 王肖肖, 张美玲, 贾利群2011 60 111101]
[16] Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 71 401
[17] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press)
[18] Mei F X, Chen X W 2000 Chin. Phys. 9 721
[19] Luo S K 2004 Chin. Phys. 13 2182
[20] Cai J L 2008 Chin. Phys. Lett. 25 1523
[21] Cai J L, Mei F X 2008 Acta Phys. Sin. 57 5369 (in Chinese) [蔡建乐, 梅凤翔2008 57 5369]
[22] Cai J L, Luo S K, Mei F X 2008 Chin. Phys. B 17 3170
[23] Zhang Y, Mei F X 2004 Acta Phys. Sin. 53 2419 (in Chinese) [张毅, 梅凤翔2004 53 2419]
[24] Luo S K, Zhang Y F 2008 Progress of Dynamics of Constrained Systems (Beijing: Science Press) (in Chinese) [罗绍凯, 张永发 2008 约束系统动力学研究进展 (北京: 科学出版社)]
[25] Fang J H 2009 Acta Phys. Sin. 58 3617 (in Chinese) [方建会2009 58 3617]
[26] Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐2009 58 22]
[27] Cai J L 2009 Acta Phys. Pol. A 115 854
[28] Xie Y L, Jia L Q 2010 Chin. Phys. Lett. 27 120201
[29] Zheng S W, Xie J F, Chen X W 2010 Acta Phys. Sin. 59 5209 (in Chinese) [郑世旺, 解佳芳, 陈向炜 2010 59 5209]
[30] Jia L Q, Sun X T, Zhang M L, Wang X X, Xie Y L 2011 Acta Phys. Sin. 60 084501 (in Chinese) [贾利群, 孙现亭, 张美玲, 王肖肖, 解银丽2011 60 084501]
[31] Jiang W A, Luo S K 2011 Acta Phys. Sin. 60 060201 (in Chinese) [姜文安, 罗绍凯 2011 60 060201]
[32] Jiang W A, Li Z J, Luo S K 2011 Chin. Phys. B 20 030202
[33] Cai J L 2012 Nonlinear Dyn. 69 487
[34] Mei F X 2001 Chin. Phys. 10 177
[35] Jia L Q, Zhang Y Y, Cui J C 2009 Journal of Yunnan University 31 52 (in Chinese) [贾利群, 张耀宇, 崔金超2009云南大学学报 31 52]
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[1] Lutzky M 1979 J. Phys. A Math. Gen. 12 973
[2] Noether A E 1918 Nachr. Akad. Math. 2 235
[3] 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)]
[4] Galiullin A S, Gafarov G G, Malaishka R P, Khwan A M 1997 Analytical Dynamics of Helmholtz, Birkhoff and Nambu Systems (Moscow: UFN) (in Russian)
[5] Zhang Y, Xue Y 2009 Chin. Q. Mech. 30 216 (in Chinese) [张毅, 薛纭2009力学季刊 30 216]
[6] Cai J L, Shi S S, Fang H J 2012 Meccanica 47 63
[7] Chen X W, Zhao Y H, Li Y M 2009 Chin. Phys. B 18 3139
[8] Cai J L, Shi S S 2012 Acta Phys. Sin. 61 030201 (in Chinese) [蔡建乐, 史生水2012 61 030201]
[9] Appell P 1953 Traité de Mécanique Rationnelle II (Paris: Gauthier-Villars) p335
[10] Xue W X 1987 Acta Mech. Sin. 19 156
[11] Luo S K 2002 Acta Phys. Sin. 51 712 (in Chinese) [罗绍凯2002 51 712]
[12] Cui J C, Zhang Y Y, Yang X F, Jia L Q 2010 Chin. Phys. B 19 030304
[13] Li Y C, Xia L L, Wang X M, Liu X W 2010 Acta Phys. Sin. 59 3639 (in Chinese) [李元成, 夏丽莉, 王小明, 刘晓巍2010 59 3639]
[14] Jia L Q, Xie Y L, Zhang Y Y, Cui J C, Yang X F 2010 Acta Phys. Sin. 59 7552 (in Chinese) [贾利群, 解银丽, 张耀宇, 崔金超, 杨新芳2010 59 7552]
[15] Yang X F, Sun X T, Wang X X, Zhang M L, Jia L Q 2011 Acta Phys. Sin. 60 111101 (in Chinese) [杨新芳, 孙现亭, 王肖肖, 张美玲, 贾利群2011 60 111101]
[16] Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 71 401
[17] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press)
[18] Mei F X, Chen X W 2000 Chin. Phys. 9 721
[19] Luo S K 2004 Chin. Phys. 13 2182
[20] Cai J L 2008 Chin. Phys. Lett. 25 1523
[21] Cai J L, Mei F X 2008 Acta Phys. Sin. 57 5369 (in Chinese) [蔡建乐, 梅凤翔2008 57 5369]
[22] Cai J L, Luo S K, Mei F X 2008 Chin. Phys. B 17 3170
[23] Zhang Y, Mei F X 2004 Acta Phys. Sin. 53 2419 (in Chinese) [张毅, 梅凤翔2004 53 2419]
[24] Luo S K, Zhang Y F 2008 Progress of Dynamics of Constrained Systems (Beijing: Science Press) (in Chinese) [罗绍凯, 张永发 2008 约束系统动力学研究进展 (北京: 科学出版社)]
[25] Fang J H 2009 Acta Phys. Sin. 58 3617 (in Chinese) [方建会2009 58 3617]
[26] Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐2009 58 22]
[27] Cai J L 2009 Acta Phys. Pol. A 115 854
[28] Xie Y L, Jia L Q 2010 Chin. Phys. Lett. 27 120201
[29] Zheng S W, Xie J F, Chen X W 2010 Acta Phys. Sin. 59 5209 (in Chinese) [郑世旺, 解佳芳, 陈向炜 2010 59 5209]
[30] Jia L Q, Sun X T, Zhang M L, Wang X X, Xie Y L 2011 Acta Phys. Sin. 60 084501 (in Chinese) [贾利群, 孙现亭, 张美玲, 王肖肖, 解银丽2011 60 084501]
[31] Jiang W A, Luo S K 2011 Acta Phys. Sin. 60 060201 (in Chinese) [姜文安, 罗绍凯 2011 60 060201]
[32] Jiang W A, Li Z J, Luo S K 2011 Chin. Phys. B 20 030202
[33] Cai J L 2012 Nonlinear Dyn. 69 487
[34] Mei F X 2001 Chin. Phys. 10 177
[35] Jia L Q, Zhang Y Y, Cui J C 2009 Journal of Yunnan University 31 52 (in Chinese) [贾利群, 张耀宇, 崔金超2009云南大学学报 31 52]
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