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

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.

Keywords: Chetaev-type nonholonomic constraints dynamics of relative motion Appell equation Lie symmetry

Received: 27 September 2012
Revised: 23 October 2012
Accepted manuscript online:

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 the Scientific Research and Innovation Plan for College Graduates of Jiangsu Province, China (Grant Nos. CXLX12_0720).

Corresponding Authors: Jia Li-Qun
E-mail: jlq0000@163.com

Cite this article:

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 2013 Chin. Phys. B 22 020201

[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)

[1]	Lie symmetry analysis and invariant solutions for the (3+1)-dimensional Virasoro integrable model Hengchun Hu(胡恒春) and Yaqi Li(李雅琦). Chin. Phys. B, 2023, 32(4): 040503.
[2]	Lie symmetry theorem of fractional nonholonomic systems Sun Yi (孙毅), Chen Ben-Yong (陈本永), Fu Jing-Li (傅景礼). Chin. Phys. B, 2014, 23(11): 110201.
[3]	Lie symmetries and exact solutions for a short-wave model Chen Ai-Yong (陈爱永), Zhang Li-Na (章丽娜), Wen Shuang-Quan (温双全). Chin. Phys. B, 2013, 22(4): 040510.
[4]	Form invariance and approximate conserved quantity of Appell equations for a weakly nonholonomic system Jia Li-Qun(贾利群), Zhang Mei-Ling(张美玲), Wang Xiao-Xiao(王肖肖), and Han Yue-Lin(韩月林) . Chin. Phys. B, 2012, 21(7): 070204.
[5]	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(王肖肖), Sun Xian-Ting(孙现亭), Zhang Mei-Ling(张美玲), Han Yue-Lin(韩月林), and Jia Li-Qun(贾利群) . Chin. Phys. B, 2012, 21(5): 050201.
[6]	Mei conserved quantity directly induced by Lie symmetry in a nonconservative Hamilton system Fang Jian-Hui(方建会), Zhang Bin(张斌), Zhang Wei-Wei(张伟伟), and Xu Rui-Li(徐瑞莉) . Chin. Phys. B, 2012, 21(5): 050202.
[7]	Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems Wang Xing-Zhong(王性忠), Fu Hao(付昊), and Fu Jing-Li(傅景礼) . Chin. Phys. B, 2012, 21(4): 040201.
[8]	Approximate solution of the magneto-hydrodynamic flow over a nonlinear stretching sheet Eerdunbuhe(额尔敦布和) and Temuerchaolu(特木尔朝鲁) . Chin. Phys. B, 2012, 21(3): 035201.
[9]	Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion Zhang Mei-Ling (张美玲), Wang Xiao-Xiao (王肖肖), Han Yue-Lin (韩月林), Jia Li-Qun (贾利群). Chin. Phys. B, 2012, 21(10): 100203.
[10]	Lie symmetry and Mei conservation law of continuum system Shi Shen-Yang(施沈阳) and Fu Jing-Li(傅景礼) . Chin. Phys. B, 2011, 20(2): 021101.
[11]	Poisson theory and integration method for a dynamical system of relative motion Zhang Yi(张毅) and Shang Mei(尚玫) . Chin. Phys. B, 2011, 20(2): 024501.
[12]	Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion Zhang Mei-Ling(张美玲), Sun Xian-Ting(孙现亭), Wang Xiao-Xiao(王肖肖), Xie Yin-Li(解银丽), and Jia Li-Qun(贾利群) . Chin. Phys. B, 2011, 20(11): 110202.
[13]	Special Lie symmetry and Hojman conserved quantity of Appell equations in a dynamical system of relative motion Xie Yin-Li(解银丽), Jia Li-Qun(贾利群), and Luo Shao-Kai(罗绍凯). Chin. Phys. B, 2011, 20(1): 010203.
[14]	A new type of conserved quantity of Lie symmetry for the Lagrange system Fang Jian-Hui(方建会). Chin. Phys. B, 2010, 19(4): 040301.
[15]	Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system Cui Jin-Chao(崔金超), Zhang Yao-Yu(张耀宇), Yang Xin-Fang(杨新芳), and Jia Li-Qun(贾利群). Chin. Phys. B, 2010, 19(3): 030304.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

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

Cite this article:

Online attention