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Chin. Phys. B, 2012, Vol. 21(10): 100203    DOI: 10.1088/1674-1056/21/10/100203
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Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion

Zhang Mei-Ling, Wang Xiao-Xiao, Han Yue-Lin, Jia Li-Qun
School of Science, Jiangnan University, Wuxi 214122, China
Abstract  Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion are studied. The definition and criterion of the Mei symmetry of Appell equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups are given. The structural equation of Mei symmetry of Appell equations and the expression of Mei conserved quantity deduced directly from Mei symmetry for a variable mass holonomic system of relative motion are gained. Finally, an example is given to illustrate the application of the results.
Keywords:  variable mass      relative motion      Appell equations      Mei conserved quantity  
Received:  16 January 2012      Revised:  28 April 2012      Published:  01 September 2012
PACS:  02.20.Sv (Lie algebras of Lie groups)  
  11.30.-j (Symmetry and conservation laws)  
  45.20.Jj (Lagrangian and Hamiltonian mechanics)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11142014 and 61178032).
Corresponding Authors:  Jia Li-Qun     E-mail:  jlq0000@163.com

Cite this article: 

Zhang Mei-Ling, Wang Xiao-Xiao, Han Yue-Lin, Jia Li-Qun Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion 2012 Chin. Phys. B 21 100203

[1] Appell P 1953 Traité de Mécanique Rationnelle II (Paris: Gauthier-Villars) p. 335
[2] Mei F X 1985 Foundations of Mechanics of Nonholonomic Systems (Beijing: Beijing Institute of Technology Press) p. 214
[3] Xu X J and Mei F X 2004 J. Beijing Inst. Technol. 23 1 (in Chinese)
[4] Luo S K 2007 Acta Phys. Sin. 56 5580 (in Chinese)
[5] Luo S K 2007 Chin. Phys. Lett. 24 2463
[6] Cai J L 2008 Acta Phys. Sin. 57 5369 (in Chinese)
[7] Chen X W 2008 Chin. Phys. B 17 3180
[8] Cai J L 2010 Chin. J. Phys. 48 728
[9] Jiang W A, Li Z J and Luo S K 2011 Chin. Phys. B 20 030202
[10] Fang J H, Xue Q Z and Zhao C Q 2002 Acta Phys. Sin. 51 2183 (in Chinese)
[11] Ge W K and Zhang Y 2004 Chin. Quar. Mech. 25 573
[12] Zhang Y, Fan C X and Mei F X 2006 Acta Phys. Sin. 55 3237 (in Chinese)
[13] Cui J C, Zhang Y Y and Jia L Q 2009 Chin. Phys. B 18 1731
[14] Xie Y L, Jia L Q and Yang X F 2011 Acta Phys. Sin. 58 2141 (in Chinese)
[15] Mei F X 2001 Chin. Phys. 10 177
[16] Luo S K 2002 Acta Phys. Sin. 51 712 (in Chinese)
[17] Xie Y L and Jia L Q 2010 Chin. Phys. Lett. 27 120201
[18] Cui J C, Zhang Y Y, Yang X F and Jia L Q 2010 Chin. Phys. B 19 030304
[19] Li Y C, Xia L L, Wang X M and Liu X W 2010 Acta Phys. Sin. 59 3639 (in Chinese)
[20] Jia L Q, Xie Y L, Zhang Y Y and Yang X F 2010 Chin. Phys. B 19 110301
[21] Jia L Q, Sun X T, Wang X X, Zhang M L and Xie Y L 2010 J. Henan Norm. Univ. (Natural Science) 33 57 (in Chinese)
[22] Luo Y P and Fu J L 2010 Chin. Phys. B 19 090304
[23] Jia L Q, Xie Y L, Zhang Y Y, Cui J C and Yang X F 2010 Acta Phys. Sin. 59 7552 (in Chinese)
[24] Zhang Y and Mei F X 2000 Chin. Sci. Bull. 45 135
[25] Zheng S W, Tang Y F and Fu J L 2006 Chin. Phys. 15 243
[26] Cai J L 2008 Chin. Phys. Lett. 25 1523
[27] Lou Z M 2008 Acta Phys. Sin. 57 1307 (in Chinese)
[28] Cai J L, Luo S K and Mei F X 2008 Chin. Phys. B 17 3170
[29] Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese)
[30] Fang J H 2009 Acta Phys. Sin. 58 3617 (in Chinese)
[31] Cai J L 2010 Int. J. Theor. Phys. 49 201
[32] Jiang W A and Luo S K 2011 Acta Phys. Sin. 60 060201 (in Chinese)
[33] Jia L Q, Sun X T, Zhang M L, Wang X X and Xie Y L 2011 Acta Phys. Sin. 60 084501 (in Chinese)
[34] Li Z J, Jiang W A and Luo S K 2012 Nonlinear Dyn. 67 445 (in Chinese)
[35] Jiang W A and Luo S K 2012 Nonlinear Dyn. 67 475
[36] Jiang W A, Li L, Li Z J and Luo S K 2012 Nonlinear Dyn. 67 1075
[37] Mei F X and Liu G L 1987 Foundations of Analytical Mechanics (Xi'an Jiaotong University Press) p. 91 (in Chinese)
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