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

doi:10.1088/1674-1056/21/5/050201

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
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 61178032).

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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) 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

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[2]	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.
[3]	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.
[4]	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.
[5]	Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems Jiang Wen-An(姜文安), Li Zhuang-Jun(李状君), and Luo Shao-Kai(罗绍凯). Chin. Phys. B, 2011, 20(3): 030202.
[6]	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.
[7]	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.
[8]	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.
[9]	Mei symmetry and Mei conserved quantity of Nielsen equations for a non-holonomic system of Chetaev's type with variable mass Yang Xin-Fang(杨新芳), Jia Li-Qun(贾利群), Cui Jin-Chao(崔金超), and Luo Shao-Kai(罗绍凯). Chin. Phys. B, 2010, 19(3): 030305.
[10]	A type of new conserved quantity deduced from Mei symmetry for Appell equations in a holonomic system with unilateral constraints Jia Li-Qun(贾利群), Xie Yin-Li(解银丽), Zhang Yao-Yu(张耀宇), and Yang Xin-Fang(杨新芳). Chin. Phys. B, 2010, 19(11): 110301.
[11]	Mei conserved quantity of the Nielsen equation for a non-Chetaev-type non-holonomic system Cui Jin-Chao(崔金超), Zhang Yao-Yu(张耀宇) , and Jia Li-Qun(贾利群). Chin. Phys. B, 2009, 18(5): 1731-1736.
[12]	Mei symmetry and Mei conserved quantity of nonholonomic systems with unilateral Chetaev type in Nielsen style Jia Li-Qun(贾利群), Xie Jia-Fang(解加芳), and Luo Shao-Kai(罗绍凯) . Chin. Phys. B, 2008, 17(5): 1560-1564.
[13]	Structure equation and Mei conserved quantity for Mei symmetry of Appell equation Jia Li-Qun(贾利群), Xie Jia-Fang(解加芳), and Zheng Shi-Wang(郑世旺) . Chin. Phys. B, 2008, 17(1): 17-22.
[14]	FORM INVARIANCE OF APPELL EQUATIONS Mei Feng-xiang (梅凤翔). Chin. Phys. B, 2001, 10(3): 177-180.

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

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