Please wait a minute...
Chin. Phys. B, 2010, Vol. 19(3): 030304    DOI: 10.1088/1674-1056/19/3/030304
GENERAL Prev   Next  

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system

Zhang Yao-Yua, Cui Jin-Chaob, Yang Xin-Fangb, Jia Li-Qunb
a Electric and Information Engineering College, Pingdingshan University, Pingdingshan 467002, China; b School of Science, Jiangnan University, Wuxi 214122, China
Abstract  Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system are investigated. Appell equations and differential equations of motion for a variable mass holonomic system are established. A new expression of the total first derivative of the function with respect of time t along the systematic motional track curve, and the definition and the criterion of Mei symmetry for Appell equations under the infinitesimal transformations of groups are given. The expressions of the structural equation and Mei conserved quantity for Mei symmetry in Appell are obtained. An example is given to illustrate the application of the results.
Keywords:  variable mass holonomic system      Mei conserved quantity      Appell equation      Mei symmetry     
Received:  31 May 2009      Published:  15 March 2010
PACS:  45.20.Jj (Lagrangian and Hamiltonian mechanics)  
  02.30.Jr (Partial differential equations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No.~10572021) and the Preparatory Research Foundation of Jiangnan University, China (Grant No.~2008LYY011).

Cite this article: 

Cui Jin-Chao, Zhang Yao-Yu, Yang Xin-Fang, Jia Li-Qun Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system 2010 Chin. Phys. B 19 030304

[1] Mei F X 1991 Advanced Analytical Mechanics (Beijing: BeijingInstitute of Technology Press) (in Chinese)
[2] Noether A E 1918 Nachr. Akad. Math. 2 235
[3] Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: BeijingInstitute of Technology Press) (in Chinese)
[4] Xu X J and Mei F X 2004 J. Beijing Inst. Technol. 23 0001(in Chinese)
[5] Zhang Y, Fan C X and Mei F X 2006 Acta Phys. Sin. 55 3237 (in Chinese)
[6] Jia L Q, Zhang Y Y, Luo S K and Cui J C 2009 Acta Phys. Sin. 58 2141 (in Chinese)
[7] Fang J H, Xue Q Z and Zhao C Q 2002 Acta Phys. Sin. 51 2183 (in Chinese)
[8] Cui J C, Zhang Y Y and Jia L Q 2009 Chin. Phys. B 18 1731
[9] Qiao Y F, Zhao S H and Li R J 2004 Chin. Phys. 13 292
[10] Ge W K and Zhang Y 2004 Chin. Quar. Mech. 25 573
[11] Lutzky M 1998 Int. J. Non-linear Mech. 33 393
[12] Mei F X 2001 Chin. Phys. 10 177
[13] Luo S K 2002 Acta Phys. Sin. 51 712 (in Chinese)
[14] Luo S K 2002 J. Changsha Univ. 16 1(in Chinese)
[15] Jia L Q, Xie J F and Zheng S W 2008 Chin. Phys. B 17 17
[16] Mei F X 2003 J. Beijing Inst. Technol. 23 0001 (in Chinese)
[17] Li R J, Qiao Y F and Meng J 2002 Acta Phys. Sin. 51 0001 (in Chinese)
[18] Luo S K and Zhang Y F 2008 Advances in the Study of Dynamicsof Constrained Systems (Beijing: Science Press) (in Chinese)
[19] Fang J H 2003 Commun. Theor. Phys. 40 269
[20] Chen X W and Mei F X 2000 Chin. Phys. 9 721
[21] Fu J L, Chen B Y and Xie F P 2008 Chin. Phys. B 17 4354
[22] Jia L Q, Cui J C, Luo S K and Yang X F 2009 Chin. Phys. Lett. 26 030303
[23] Jia L Q, Zhang Y Y and Cui J C 2009 J. Yunnan Univ. 31 52 (in Chinese)
[1] Mei symmetry and conservation laws of discrete nonholonomic dynamical systems with regular and irregular lattices
Zhao Gang-Ling, Chen Li-Qun, Fu Jing-Li, Hong Fang-Yu. Chin. Phys. B, 2013, 22(3): 030201.
[2] 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.
[3] A type of conserved quantity of Mei symmetry of Nielsen equations for a holonomic system
Cui Jin-Chao, Han Yue-Lin, Jia Li-Qun. Chin. Phys. B, 2012, 21(8): 080201.
[4] Mei symmetry and conserved quantities in Kirchhoff thin elastic rod statics
Wang Peng, Xue Yun, Liu Yu-Lu. Chin. Phys. B, 2012, 21(7): 070203.
[5] 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.
[6] Mei symmetry and Mei conserved quantity of the Appell equation in a dynamical system of relative motion with non-Chetaev nonholonomic constraints
Wang Xiao-Xiao,Sun Xian-Ting,Zhang Mei-Ling,Han Yue-Lin,Jia Li-Qun. Chin. Phys. B, 2012, 21(5): 050201.
[7] 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.
[8] Noether–Mei symmetry of discrete mechanico-electrical system
Zhang Wei-Wei, Fang Jian-Hui. Chin. Phys. B, 2012, 21(11): 110201.
[9] 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.
[10] Lie–Mei symmetry and conserved quantities of the Rosenberg problem
Liu Xiao-Wei, Li Yuan-Cheng. Chin. Phys. B, 2011, 20(7): 070204.
[11] Perturbation to Mei symmetry and Mei adiabatic invariants for discrete generalized Birkhoffian system
Zhang Ke-Jun, Fang Jian-Hui, Li Yan. Chin. Phys. B, 2011, 20(5): 054501.
[12] A new type of conserved quantity of Mei symmetry for the motion of mechanico–electrical coupling dynamical systems
Zhao Li, Fu Jing-Li, Chen Ben-Yong. Chin. Phys. B, 2011, 20(4): 040201.
[13] 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.
[14] Lie symmetry and Mei conservation law of continuum system
Shi Shen-Yang, Fu Jing-Li. Chin. Phys. B, 2011, 20(2): 021101.
[15] Conformal invariance and conserved quantities of Birkhoff systems under second-class Mei symmetry
Luo Yi-Ping, Fu Jing-Li. Chin. Phys. B, 2011, 20(2): 021102.
No Suggested Reading articles found!