Please wait a minute...
Chin. Phys. B, 2012, Vol. 21(5): 050201    DOI: 10.1088/1674-1056/21/5/050201
GENERAL   Next  

Mei symmetry and Mei conserved quantity of the Appell equation in a dynamical system of relative motion with non-Chetaev nonholonomic constraints

Wang Xiao-Xiaoa,Sun Xian-Tingb,Zhang Mei-Linga,Han Yue-Lina,Jia Li-Quna
1. School of Science, Jiangnan University, Wuxi 214122, China;
2. School of Electric and Information Engineering, Pingdingshan University, Pingdingshan 467002, China
Abstract  The Mei symmetry and the Mei conserved quantity of Appell equations in a dynamical system of relative motion with non-Chetaev nonholonomic constraints are studied. The differential equations of motion of the Appell equation for the system, the definition and the criterion of the Mei symmetry, and the expression of the Mei conserved quantity deduced directly from the Mei symmetry for the system are obtained. An example is given to illustrate the application of the results.
Keywords:  non-Chetaev nonholonomic constrained system      dynamics of relative motion      Appell equation      Mei conserved quantity  
Received:  22 November 2011      Revised:  27 April 2012      Published:  01 April 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 No. 11142014 and 61178032).

Cite this article: 

Wang Xiao-Xiao,Sun Xian-Ting,Zhang Mei-Ling,Han Yue-Lin,Jia Li-Qun Mei symmetry and Mei conserved quantity of the Appell equation in a dynamical system of relative motion with non-Chetaev nonholonomic constraints 2012 Chin. Phys. B 21 050201

[1] Wu H B and Mei F X 2006 Acta Phys. Sin. 55 3825 (in Chinese)
[2] Li Y C, Zhang Y and Liang J H 2001 Acta Mechanica Solida Sinica 22 75
[3] Zhang Y and Mei F X 2004 Acta Phys. Sin. 53 661 (in Chinese)
[4] Ge W K 2002 Acta Phys. Sin. 51 1156 (in Chinese)
[5] Zhang Y and Mei F X 2004 Acta Phys. Sin. 53 2419 (in Chinese)
[6] Fu J L, Nie N M and Huang J F 2009 Chin. Phys. B 18 2634
[7] Shang M and Mei F X 2007 Chin. Phys. B 16 3161
[8] Jiang W A and Luo S K 2011 Nonlinear Dyn. 67 475
[9] Xie Y L, Jia L Q and Yang X F 2011 Acta Phys. Sin. 60 030201 (in Chinese)
[10] Li Z J, Jiang W A and Luo S K 2011 Nonlinear Dyn. 67 445
[11] Jiang W A, Li L, Li Z J and Luo S K 2012 Nonlinear Dyn. 67 1075
[12] Luo S K 2003 Acta Phys. Sin. 52 2941 (in Chinese)
[13] Zhang Y 2007 Acta Phys. Sin. 56 3054 (in Chinese)
[14] Mei F X and Shang M 2000 Acta Phys. Sin. 49 1901 (in Chinese)
[15] Chen X W, Liu C M and Li Y M 2006 Chin. Phys. B 15 470
[16] Cai J L and Mei F X 2008 Acta Phys. Sin. 57 5369 (in Chinese)
[17] Cai J L, Luo S K and Mei F X 2008 Chin. Phys. B 17 3170
[18] Cai J L 2009 Acta Physica Polonica A 115 854
[19] Wu H B, Xu X J, Wang S Y and Mei F X 2004 Journal of Beijing Institute of Technology 24 469 (in Chinese)
[20] Lou Z M 2004 Acta Phys. Sin. 53 2046 (in Chinese)
[21] Fang J H 2009 Acta Phys. Sin. 58 3617 (in Chinese)
[22] Cai J L 2010 Acta Physica Polonica A 117 445
[23] Zheng S W, Xie J F and Chen X W 2010 Acta Phys. Sin. 59 5209 (in Chinese)
[24] Zheng S W, Xie J F and Chen W C 2008 Chin. Phys. Lett. 25 809
[25] Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese)
[26] Jiang W A, Li Z J and Luo S K 2011 Chin. Phys. B 20 030202
[27] Jiang W A and Luo S K 2011 Acta Phys. Sin. 60 060201 (in Chinese)
[28] Mei F X 2000 Journal of Beijing Institute of Technology 9 120 (in Chinese)
[29] Mei F X 1988 Analytical Mechanics Topics (Beijing:Beijing Institute of Technology Press) (in Chinese)
[30] Mei F X, Liu D and Luo Y 1991 Advanced Analytical Mechanics (Beijing:Beijing Institute of Technology Press) (in Chinese)
[31] Mei F X 2001 Chin.Phys. 10 177
[32] Li R J, Qiao Y F and Meng J 2002 Acta Phys. Sin. 51 1 (in Chinese)
[33] Luo S K 2002 Acta Phys. Sin. 51 712 (in Chinese)
[34] Luo S K and Zhang Y F 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing:Science Press) (in Chinese)
[35] Jia L Q, Xie Y L and Luo S K 2011 Acta Phys. Sin. 60 040201 (in Chinese)
[36] Yang X F, Sun X T, Wang X X, Zhang M L and Jia L Q 2011 Acta Phys. Sin. 60 111101 (in Chinese)
[37] Li Y C, Xia L L, Wang X M and Liu X W 2010 Acta Phys. Sin. 59 3639 (in Chinese)
[38] Jia L Q, Xie Y L, Zhang Y Y, Cui J C and Yang X F 2010 Acta Phys. Sin. 59 7552 (in Chinese)
[1] Lie symmetry and its generation of conserved quantity of Appell equation in a dynamical system of the relative motion with Chetaev-type nonholonomic constraints
Wang Xiao-Xiao, Han Yue-Lin, Zhang Mei-Ling, Jia Li-Qun. Chin. Phys. B, 2013, 22(2): 020201.
[2] Form invariance and approximate conserved quantity of Appell equations for a weakly nonholonomic system
Jia Li-Qun, Zhang Mei-Ling, Wang Xiao-Xiao, Han Yue-Lin. Chin. Phys. B, 2012, 21(7): 070204.
[3] Mei conserved quantity directly induced by Lie symmetry in a nonconservative Hamilton system
Fang Jian-Hui,Zhang Bin,Zhang Wei-Wei,Xu Rui-Li. Chin. Phys. B, 2012, 21(5): 050202.
[4] 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. Chin. Phys. B, 2012, 21(10): 100203.
[5] Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems
Jiang Wen-An, Li Zhuang-Jun, Luo Shao-Kai. Chin. Phys. B, 2011, 20(3): 030202.
[6] Poisson theory and integration method for a dynamical system of relative motion
Zhang Yi, Shang Mei. Chin. Phys. B, 2011, 20(2): 024501.
[7] Special Lie symmetry and Hojman conserved quantity of Appell equations in a dynamical system of relative motion
Xie Yin-Li, Jia Li-Qun, Luo Shao-Kai. Chin. Phys. B, 2011, 20(1): 010203.
[8] Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system
Cui Jin-Chao, Zhang Yao-Yu, Yang Xin-Fang, Jia Li-Qun. Chin. Phys. B, 2010, 19(3): 030304.
[9] A type of new conserved quantity deduced from Mei symmetry for Appell equations in a holonomic system with unilateral constraints
Jia Li-Qun, Xie Yin-Li, Zhang Yao-Yu, Yang Xin-Fang. Chin. Phys. B, 2010, 19(11): 110301.
[10] Mei conserved quantity of Nielsen equation for anon-Chetaev-type non-holonomic system
Cui Jin-Chao, Zhang Yao-Yu, Jia Li-Qun. Chin. Phys. B, 2009, 18(5): 1731-1736.
[11] Structure equation and Mei conserved quantity for Mei symmetry of Appell equation
Xie Jia-Fang, Zheng Shi-Wang, Jia Li-Qun. Chin. Phys. B, 2008, 17(1): 17-22.
[12] FORM INVARIANCE OF APPELL EQUATIONS
Mei Feng-xiang. Chin. Phys. B, 2001, 10(3): 177-180.
No Suggested Reading articles found!