Lie symmetry and its generation of conserved quantity of Appell equation in a dynamical system of the relative motion with Chetaev-type nonholonomic constraints

doi:10.1088/1674-1056/22/2/020201

中国物理B ›› 2013, Vol. 22 ›› Issue (2): 20201-020201.doi: 10.1088/1674-1056/22/2/020201

• GENERAL • 下一篇

Lie symmetry and its generation of conserved quantity of Appell equation in a dynamical system of the relative motion with Chetaev-type nonholonomic constraints

王肖肖, 韩月林, 张美玲, 贾利群

School of Science, Jiangnan University, Wuxi 214122, China

收稿日期:2012-09-27 修回日期:2012-10-23 出版日期:2013-01-01 发布日期:2013-01-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11142014) and the Scientific Research and Innovation Plan for College Graduates of Jiangsu Province, China (Grant Nos. CXLX12_0720).

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 (王肖肖), Han Yue-Lin (韩月林), Zhang Mei-Ling (张美玲), Jia Li-Qun (贾利群)

School of Science, Jiangnan University, Wuxi 214122, China

Received:2012-09-27 Revised:2012-10-23 Online:2013-01-01 Published:2013-01-01
Contact: Jia Li-Qun E-mail:jlq0000@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11142014) and the Scientific Research and Innovation Plan for College Graduates of Jiangsu Province, China (Grant Nos. CXLX12_0720).

摘要/Abstract

摘要： Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied. The differential equations of motion of the Appell equation for the system, the definition and criterion of Lie symmetry, the condition and the expression of generalized Hojman conserved quantity deduced from Lie symmetry for the system are obtained. The condition and the expression of Hojman conserved quantity deduced from special Lie symmetry for the system under invariable time are further obtained. An example is given to illustrate the application of the results.

关键词: Chetaev-type nonholonomic constraints, dynamics of relative motion, Appell equation, Lie symmetry

Abstract: Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied. The differential equations of motion of the Appell equation for the system, the definition and criterion of Lie symmetry, the condition and the expression of generalized Hojman conserved quantity deduced from Lie symmetry for the system are obtained. The condition and the expression of Hojman conserved quantity deduced from special Lie symmetry for the system under invariable time are further obtained. An example is given to illustrate the application of the results.

Key words: Chetaev-type nonholonomic constraints, dynamics of relative motion, Appell equation, Lie symmetry

中图分类号: (Lie algebras of Lie groups)

02.20.Sv

11.30.-j (Symmetry and conservation laws) 45.20.Jj (Lagrangian and Hamiltonian mechanics)

王肖肖, 韩月林, 张美玲, 贾利群. Lie symmetry and its generation of conserved quantity of Appell equation in a dynamical system of the relative motion with Chetaev-type nonholonomic constraints[J]. 中国物理B, 2013, 22(2): 20201-020201.

Wang Xiao-Xiao (王肖肖), Han Yue-Lin (韩月林), Zhang Mei-Ling (张美玲), Jia Li-Qun (贾利群). Lie symmetry and its generation of conserved quantity of Appell equation in a dynamical system of the relative motion with Chetaev-type nonholonomic constraints[J]. Chin. Phys. B, 2013, 22(2): 20201-020201.

参考文献 38

[1]	Ge W K 2002 Acta Phys. Sin. 51 1156 (in Chinese)
[2]	Zhang Y and Mei F X 2004 Acta Phys. Sin. 53 2419 (in Chinese)
[3]	Wu H B and Mei F X 2006 Acta Phys. Sin. 55 3825 (in Chinese)
[4]	Zheng S W, Tang Y F and Fu J L 2006 Chin. Phys. 15 243
[5]	Shang M and Mei F X 2007 Chin. Phys. 16 3161
[6]	Fu J L, Nie N M, Huang J F, Jiménez S, Tang Y F, Vázquez L and Zhao W J 2009 Chin. Phys. B 18 2634
[7]	Mei F X and Shang M 2000 Acta Phys. Sin. 49 1901 (in Chinese)
[8]	Luo S K 2003 Acta Phys. Sin. 52 2941 (in Chinese)
[9]	Chen X W, Liu C M and Li Y M 2006 Chin. Phys. 15 470
[10]	Luo S K 2007 Chin Phys. Lett. 24 2463
[11]	Zhang Y 2007 Acta Phys. Sin. 56 3054 (in Chinese)
[12]	Cai J L and Mei F X 2008 Acta Phys. Sin. 57 5369 (in Chinese)
[13]	Cai J L, Luo S K and Mei F X 2008 Chin. Phys. B 17 3170
[14]	Cai J L 2008 Chin. Phys. Lett. 25 1523
[15]	Fang J H 2010 Chin. Phys. B 19 40301
[16]	Xie Y L, Jia L Q and Yang X F 2011 Acta Phys. Sin. 60 030201 (in Chinese)
[17]	Mei F X 1998 Analytical Mechanics Topics (Beijing: Beijing Institute of Technology Press)
[18]	Lou Z M 2004 Acta Phys. Sin. 53 2046 (in Chinese)
[19]	Zheng S W, Xie J F and Chen W C 2008 Chin. Phys. Lett. 25 809
[20]	Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese)
[21]	Wu H B and Mei F X 2009 Chin. Phys. B 18 3145
[22]	Fang J H 2009 Acta Phys. Sin. 58 3617 (in Chinese)
[23]	Zheng S W, Xie J F, Chen X W and Du X L 2010 Acta Phys. Sin. 59 5209 (in Chinese)
[24]	Jiang W A, Li Z J and Luo S K 2011 Chin. Phys. B 20 030202
[25]	Jiang W A and Luo S K 2011 Acta Phys. Sin. 60 060201 (in Chinese)
[26]	Cai J L 2011 Nonlinear Dyn. 69 487
[27]	Mei F X, Liu D and Luo Y 1991 Advanced Analytical Mechanics (Beijing: Beijing Institute of Technology Press)
[28]	Mei F X 2001 Chin. Phys. 10 177
[29]	Li R J, Qiao Y F and Meng J 2002 Acta Phys. Sin. 51 1 (in Chinese)
[30]	Luo S K 2002 Acta Phys. Sin. 51 712 (in Chinese)
[31]	Luo S K 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing: Science Press)
[32]	Jia L Q, Xie J F and Zheng S W 2008 Chin. Phys. B 17 17
[33]	Li Y C, Xia L L, Wang X M and Liu X W 2010 Acta Phys. Sin. 59 3639 (in Chinese)
[34]	Jia L Q, Xie Y L, Zhang Y Y, Cui J C and Yang X F 2010 Acta Phys. Sin. 59 7552 (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]	Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press)
[38]	Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press)

Lie symmetry and its generation of conserved quantity of Appell equation in a dynamical system of the relative motion with Chetaev-type nonholonomic constraints

Lie symmetry and its generation of conserved quantity of Appell equation in a dynamical system of the relative motion with Chetaev-type nonholonomic constraints

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