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The conformal invariance and Hojman conserved quantity of Lie symmetry for Appell equations in a holonomic system are studied. Under the special infinitesimal transformations in which the time is not variable, the Lie symmetry and conformal invariance of differential equations of motion for a holonomic system are defined, and the determining equations of the conformal invariance of Lie symmetry and the Hojman conserved quantity for the system are given. Finally, an example is presented to illustrate the application of the results.
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Keywords:
- Appell equation /
- Lie symmetry /
- conformal invariance /
- Hojman conserved quantity
[1] Mei F X, Wu H B 2010 Chin. Phys. B 19 050301
[2] Xie Y L, Yang X F, Jia L Q 2011 Commun. Theor. Phys. 55 111
[3] Wang X X, Sun X T, Zhang M L, Xie Y L, Jia L Q 2012 Acta Phys. Sin. 61 064501 (in Chinese) [王肖肖, 孙现亭, 张美玲, 解银丽, 贾利群 2012 61 064501]
[4] Zhang Y 2008 Acta Phys. Sin. 57 5374 (in Chinese) [张毅 2008 57 5374]
[5] Jia L Q, Wang X X, Zhang M L, Han Y L 2012 Nonlinear Dyn. 69 1807
[6] Luo S K 2007 Acta Phys. Sin. 56 5580 (in Chinese) [罗绍凯 2007 56 5580]
[7] Zhang M L, Wang X X, Han Y L, Jia L Q 2012 J. Yunnan Univ. (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 (自然科学版) 34 664]
[8] Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 73 357
[9] Ge W K 2008 Acta Phys. Sin. 57 6714 (in Chinese) [葛伟宽 2008 57 6714]
[10] 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]
[11] Fang J H 2010 Chin. Phys. B 19 040301
[12] Zheng S W, Xie J F, Chen X W, Du X L 2010 Acta Phys. Sin. 59 5209 (in Chinese) [郑世旺, 解加芳, 陈向炜, 杜雪莲 2010 59 5209]
[13] Xie Y L, Jia L Q 2010 Chin Phys. Lett. 27 120201
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[15] Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 58 22]
[16] Wu H B, Mei F X 2009 Chin. Phys. B 18 3145
[17] Cai J L 2009 Acta. Phys. Pol. A 115 854
[18] Cai J L 2010 Acta. Phys. Pol. A 117 445
[19] Jiang W A, Luo S K 2012 Nonlinear Dyn. 67 475
[20] Jiang W A, Li Z J, Luo S K 2011 Chin. Phys. B 20 030202
[21] Galiullin A S, Gafarov G G, Malaishka R P, Khwan A M 1997 Analytical Dynamics of Helmholtz Birkhoff and Nambu Systems (Moscow: UFN) p183 (in Russian)
[22] Zhang Y, Xue Y 2009 Chin. Q. Mech. 30 216 (in Chinese) [张毅, 薛纭 2009 力学季刊 30 216]
[23] Cai J L, Shi S S, Fang H J 2012 Meccanica 47 63
[24] 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]
[25] Chen X W, Zhao Y H, Li Y M 2009 Chin. Phys. B 18 3139
[26] Cai J L, Shi S S 2012 Acta Phys. Sin. 61 030201 (in Chinese) [蔡建乐, 史生水 2012 61 030201]
[27] Appell P 1953 Traité de Mécanique Rationnelle Ⅱ (Paris: Gauthier-Villars) p335
[28] Xue W X 1987 Acta Mech. Sin. 3 354
[29] Cai J L 2012 Nonlinear Dyn. 69 487
[30] Cui J C, Zhang Y Y, Yang X F, Jia L Q 2010 Chin. Phys. B 19 030304
[31] 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]
[32] 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]
[33] Jiang W A, Luo S K 2011 Acta Phys. Sin. 60 060201 (in Chinese) [姜文安, 罗绍凯 2011 60 060201]
[34] Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 71 401
[35] Mei F X, Chen X W 2000 Chin. Phys. 9 721
[36] Wang X X, Han Y L, Zhang M L, Jia L Q 2013 Chin. Phys. B 22 020201
[37] Cai J L 2008 Chin. Phys. Lett. 25 1523
[38] Han Y L, Wang X X, Zhang M L, Jia L Q 2014 J. Mech. 30 21
[39] Fang J H 2009 Acta Phys. Sin. 58 3617 (in Chinese) [方建会 2009 58 3617]
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[1] Mei F X, Wu H B 2010 Chin. Phys. B 19 050301
[2] Xie Y L, Yang X F, Jia L Q 2011 Commun. Theor. Phys. 55 111
[3] Wang X X, Sun X T, Zhang M L, Xie Y L, Jia L Q 2012 Acta Phys. Sin. 61 064501 (in Chinese) [王肖肖, 孙现亭, 张美玲, 解银丽, 贾利群 2012 61 064501]
[4] Zhang Y 2008 Acta Phys. Sin. 57 5374 (in Chinese) [张毅 2008 57 5374]
[5] Jia L Q, Wang X X, Zhang M L, Han Y L 2012 Nonlinear Dyn. 69 1807
[6] Luo S K 2007 Acta Phys. Sin. 56 5580 (in Chinese) [罗绍凯 2007 56 5580]
[7] Zhang M L, Wang X X, Han Y L, Jia L Q 2012 J. Yunnan Univ. (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 (自然科学版) 34 664]
[8] Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 73 357
[9] Ge W K 2008 Acta Phys. Sin. 57 6714 (in Chinese) [葛伟宽 2008 57 6714]
[10] 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]
[11] Fang J H 2010 Chin. Phys. B 19 040301
[12] Zheng S W, Xie J F, Chen X W, Du X L 2010 Acta Phys. Sin. 59 5209 (in Chinese) [郑世旺, 解加芳, 陈向炜, 杜雪莲 2010 59 5209]
[13] Xie Y L, Jia L Q 2010 Chin Phys. Lett. 27 120201
[14] Luo S K 2002 Acta Phys. Sin. 51 712 (in Chinese) [罗绍凯 2002 51 712]
[15] Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 58 22]
[16] Wu H B, Mei F X 2009 Chin. Phys. B 18 3145
[17] Cai J L 2009 Acta. Phys. Pol. A 115 854
[18] Cai J L 2010 Acta. Phys. Pol. A 117 445
[19] Jiang W A, Luo S K 2012 Nonlinear Dyn. 67 475
[20] Jiang W A, Li Z J, Luo S K 2011 Chin. Phys. B 20 030202
[21] Galiullin A S, Gafarov G G, Malaishka R P, Khwan A M 1997 Analytical Dynamics of Helmholtz Birkhoff and Nambu Systems (Moscow: UFN) p183 (in Russian)
[22] Zhang Y, Xue Y 2009 Chin. Q. Mech. 30 216 (in Chinese) [张毅, 薛纭 2009 力学季刊 30 216]
[23] Cai J L, Shi S S, Fang H J 2012 Meccanica 47 63
[24] 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]
[25] Chen X W, Zhao Y H, Li Y M 2009 Chin. Phys. B 18 3139
[26] Cai J L, Shi S S 2012 Acta Phys. Sin. 61 030201 (in Chinese) [蔡建乐, 史生水 2012 61 030201]
[27] Appell P 1953 Traité de Mécanique Rationnelle Ⅱ (Paris: Gauthier-Villars) p335
[28] Xue W X 1987 Acta Mech. Sin. 3 354
[29] Cai J L 2012 Nonlinear Dyn. 69 487
[30] Cui J C, Zhang Y Y, Yang X F, Jia L Q 2010 Chin. Phys. B 19 030304
[31] 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]
[32] 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]
[33] Jiang W A, Luo S K 2011 Acta Phys. Sin. 60 060201 (in Chinese) [姜文安, 罗绍凯 2011 60 060201]
[34] Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 71 401
[35] Mei F X, Chen X W 2000 Chin. Phys. 9 721
[36] Wang X X, Han Y L, Zhang M L, Jia L Q 2013 Chin. Phys. B 22 020201
[37] Cai J L 2008 Chin. Phys. Lett. 25 1523
[38] Han Y L, Wang X X, Zhang M L, Jia L Q 2014 J. Mech. 30 21
[39] Fang J H 2009 Acta Phys. Sin. 58 3617 (in Chinese) [方建会 2009 58 3617]
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