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Generalized Lie symmetry and generalized Hojman conserved quantity of Appell equations for a variable mass holonomic system in relative motion are studied. The determining equation of generalized Lie symmetry of Appell equations for a variable mass holonomic system in relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from generalized Lie symmetry for a variable mass holonomic system in relative motion is gained. Finally, the problem of dynamical system with three degree of freedom is studied by using the results of this paper.
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Keywords:
- relative motion /
- variable mass /
- generalized Lie symmetry /
- generalized Hojman conserved quantity
[1] Cai J L, Shi S S, Fang H J, Xu J 2012 Meccanica 47 63
[2] Huang W L, Cai J L 2012 Acta Mech. 223 433
[3] Luo S K, Li Z J, Li L 2012 Acta Mechanica 223 2621
[4] Cai J L 2012 Nonlinear Dyn. 69 487
[5] Jia L Q, Wang X X, Zhang M L, Han Y L 2012 Nonlinear Dyn. 69 1807
[6] Li Z J, Luo S K 2012 Nonlinear Dyn. 70 1117
[7] Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 71 401
[8] Luo S K, Li L 2013 Nonlinear Dyn. 73 339
[9] Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 73 357
[10] Luo S K, Li L 2013 Nonlinear Dyn. 73 639
[11] Luo S K, Li Z J, Peng W, Li L 2013 Acta Mechanica. 224 71
[12] Li L, Luo S kai 2013 Acta Mechanica 224 1757
[13] Lou Z M, Mei F X, Chen Z D 2012 Acta Phys. Sin. 61 110204 (in Chinese) [楼智美, 梅凤翔, 陈子栋 2012 61 110204]
[14] Chen X W, Liu C M, Li Y M 2006 Chin. Phys. 15 470
[15] Xie Y L, Jia L Q, Luo Shao-Kai 2011 Chin. Phys. B 20 010203
[16] Jia L Q, Han Y L, Zhang M L, Wang X X 2013 Journal of Pingdingshan University 28(2) 27 (in Chinese) [贾利群, 韩月林, 张美玲, 王肖肖 2013 平顶山学院学报 28(2) 27]
[17] Mei F, X 2000 Beijing Inst.Technol. 9 120
[18] Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 58 22]
[19] Li Y C, Xia L L, Wang X M, Liu X W 2010 Acta Phys. Sin. 59 3639 (in Chinese) [李元成, 夏莉丽, 王小明, 刘晓巍 2010 59 3639]
[20] Zheng S W, Jia L Q, Yu H S 2006 Chin. Phys. 15 1399
[21] Jia L Q, Xie Y L, Zhang Y Y, Yang X F 2010 Chin. Phys. B 19 110306
[22] Wang X X, Zhang M L, Han Y L, Jia L Q 2012 Acta Phys. Sin. 61 200203 (in Chinese) [王肖肖, 张美玲, 韩月林, 贾利群 2012 61 200203]
[23] Sun X T, Han Y L, Wang X X, Zhang M L, Jia L Q 2012 Acta Phys. Sin. 61 200204 (in Chinese) [孙现亭, 韩月林, 王肖肖, 张美玲, 贾利群 2012 61 200204]
[24] Hojman S A 1992 J. Phys. A: Math. Gen. 25 291
[25] Xu X J, Mei F X, Zhang Y F 2006 Chin. Phys. 15 19
[26] Ge W K, Zhang Y 2005 Acta Phys. Sin. 54 4985 (in Chinese) [葛伟宽, 张毅 2005 54 4985]
[27] Wang X X, Sun X T, Zhang M L, Xie Y L, Jia L Q 2011 Chin. Phys. B 20 124501
[28] Lin P, Fang J H, Pang T 2008 Chin. Phys. B 17 4361
[29] Ding N, Fang J H, Chen X X 2008 Chin. Phys. B 17 1967
[30] Fang J H 2010 Chin. Phys. B 19 040301
[31] Zhang N X, Fang J H, Lin P, Pang T 2008 Commun. Theor. Phys. 49 1145
[32] Zhang M J, Fang J H, Lin P, Lu K, Pang T 2009 Commun. Theor. Phys. 52 561
[33] Xia L L, Li Y C, Wang X J 2009 Commun. Theor. Phys. 51 1073
[34] Zhang M L, Sun X T, Wang X X, Xie Y L, Jia L Q 2011 Chin. Phys. B 20 110202
[35] Zhang M L, Wang X X, Han Y L, Jia L Q 2012 Chin. Phys. B 21 100203
[36] Zhang M L, Wang X X, Han Y L, Jia L Q 2012 Journal of Yunnan University 34 664 (in Chinese) [张美玲, 王肖肖, 韩月林, 贾利群 2013 云南大学学报 34 664]
[37] Wang X X, Sun X T, Zhang M L, Han Y L, Jia L Q 2012 Chin. Phys. B 21 050201
[38] Wang X X, Han Y L, Zhang M L, Jia L Q 2013 Chin. Phys. B 22 020201
[39] 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)]
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[1] Cai J L, Shi S S, Fang H J, Xu J 2012 Meccanica 47 63
[2] Huang W L, Cai J L 2012 Acta Mech. 223 433
[3] Luo S K, Li Z J, Li L 2012 Acta Mechanica 223 2621
[4] Cai J L 2012 Nonlinear Dyn. 69 487
[5] Jia L Q, Wang X X, Zhang M L, Han Y L 2012 Nonlinear Dyn. 69 1807
[6] Li Z J, Luo S K 2012 Nonlinear Dyn. 70 1117
[7] Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 71 401
[8] Luo S K, Li L 2013 Nonlinear Dyn. 73 339
[9] Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 73 357
[10] Luo S K, Li L 2013 Nonlinear Dyn. 73 639
[11] Luo S K, Li Z J, Peng W, Li L 2013 Acta Mechanica. 224 71
[12] Li L, Luo S kai 2013 Acta Mechanica 224 1757
[13] Lou Z M, Mei F X, Chen Z D 2012 Acta Phys. Sin. 61 110204 (in Chinese) [楼智美, 梅凤翔, 陈子栋 2012 61 110204]
[14] Chen X W, Liu C M, Li Y M 2006 Chin. Phys. 15 470
[15] Xie Y L, Jia L Q, Luo Shao-Kai 2011 Chin. Phys. B 20 010203
[16] Jia L Q, Han Y L, Zhang M L, Wang X X 2013 Journal of Pingdingshan University 28(2) 27 (in Chinese) [贾利群, 韩月林, 张美玲, 王肖肖 2013 平顶山学院学报 28(2) 27]
[17] Mei F, X 2000 Beijing Inst.Technol. 9 120
[18] Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 58 22]
[19] Li Y C, Xia L L, Wang X M, Liu X W 2010 Acta Phys. Sin. 59 3639 (in Chinese) [李元成, 夏莉丽, 王小明, 刘晓巍 2010 59 3639]
[20] Zheng S W, Jia L Q, Yu H S 2006 Chin. Phys. 15 1399
[21] Jia L Q, Xie Y L, Zhang Y Y, Yang X F 2010 Chin. Phys. B 19 110306
[22] Wang X X, Zhang M L, Han Y L, Jia L Q 2012 Acta Phys. Sin. 61 200203 (in Chinese) [王肖肖, 张美玲, 韩月林, 贾利群 2012 61 200203]
[23] Sun X T, Han Y L, Wang X X, Zhang M L, Jia L Q 2012 Acta Phys. Sin. 61 200204 (in Chinese) [孙现亭, 韩月林, 王肖肖, 张美玲, 贾利群 2012 61 200204]
[24] Hojman S A 1992 J. Phys. A: Math. Gen. 25 291
[25] Xu X J, Mei F X, Zhang Y F 2006 Chin. Phys. 15 19
[26] Ge W K, Zhang Y 2005 Acta Phys. Sin. 54 4985 (in Chinese) [葛伟宽, 张毅 2005 54 4985]
[27] Wang X X, Sun X T, Zhang M L, Xie Y L, Jia L Q 2011 Chin. Phys. B 20 124501
[28] Lin P, Fang J H, Pang T 2008 Chin. Phys. B 17 4361
[29] Ding N, Fang J H, Chen X X 2008 Chin. Phys. B 17 1967
[30] Fang J H 2010 Chin. Phys. B 19 040301
[31] Zhang N X, Fang J H, Lin P, Pang T 2008 Commun. Theor. Phys. 49 1145
[32] Zhang M J, Fang J H, Lin P, Lu K, Pang T 2009 Commun. Theor. Phys. 52 561
[33] Xia L L, Li Y C, Wang X J 2009 Commun. Theor. Phys. 51 1073
[34] Zhang M L, Sun X T, Wang X X, Xie Y L, Jia L Q 2011 Chin. Phys. B 20 110202
[35] Zhang M L, Wang X X, Han Y L, Jia L Q 2012 Chin. Phys. B 21 100203
[36] Zhang M L, Wang X X, Han Y L, Jia L Q 2012 Journal of Yunnan University 34 664 (in Chinese) [张美玲, 王肖肖, 韩月林, 贾利群 2013 云南大学学报 34 664]
[37] Wang X X, Sun X T, Zhang M L, Han Y L, Jia L Q 2012 Chin. Phys. B 21 050201
[38] Wang X X, Han Y L, Zhang M L, Jia L Q 2013 Chin. Phys. B 22 020201
[39] 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)]
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