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Abstract
This paper studies the Lagrange symmetry of a dynamical system of relative motion. The definition and the criterion of the symmetry of the system are established. The condition under which there exists a conserved quantity and the form of the conserved quantity are obtained.

Keywords:
dynamics of relative motion/

Lagrange symmetry/

conserved quantity
Authors and contacts
Mei Feng-Xiang,

Wu Hui-Bin

1.
References

Cited By

[1]	Zhang Yi.Symmetry of Birkhoffians and conserved quantity for a relativistic mechanical system. Acta Physica Sinica, 2012, 61(21): 214501.doi:10.7498/aps.61.214501
[2]	Zhang Bin, Fang Jian-Hui, Zhang Ke-Jun.Symmetry and conserved quantity of Lagrangians for nonholonomic variable mass system. Acta Physica Sinica, 2012, 61(2): 021101.doi:10.7498/aps.61.021101
[3]	Wang Xiao-Xiao, Zhang Mei-Ling, Han Yue-Lin, Jia Li-Qun.Mei symmetry and Mei conserved quantity of Nielsen equation in a dynamical system of the relative motion with nonholonomic constraint of Chetaev's type. Acta Physica Sinica, 2012, 61(20): 200203.doi:10.7498/aps.61.200203
[4]	Wang Xiao-Xiao, Sun Xian-Ting, Zhang Mei-Ling, Xie Yin-Li, Jia Li-Qun.Noether symmetry and Noether conserved quantity of Nielsen equation in a dynamical system of the relative motion with nonholonomic constraint of Chetaev's type. Acta Physica Sinica, 2012, 61(6): 064501.doi:10.7498/aps.61.064501
[5]	Luo Shao-Kai, Jia Li-Qun, Xie Yin-Li.Mei conserved quantity deduced from Mei symmetry of Appell equation in a dynamical system of relative motion. Acta Physica Sinica, 2011, 60(4): 040201.doi:10.7498/aps.60.040201
[6]	Xie Yin-Li, Jia Li-Qun, Yang Xin-Fang.Lie symmetry and Hojman conserved quantity of Nielsen equation in a dynamical system of the relative motion. Acta Physica Sinica, 2011, 60(3): 030201.doi:10.7498/aps.60.030201
[7]	Zhang Yi, Xue Yun, Ge Wei-Kuan.Symmetries and conserved quantities of the Rosenberg problem. Acta Physica Sinica, 2010, 59(7): 4434-4436.doi:10.7498/aps.59.4434
[8]	Liu Yang-Kui.A kind of conserved quantity of Mei symmetry for general holonomic mechanical systems. Acta Physica Sinica, 2010, 59(1): 7-10.doi:10.7498/aps.59.7
[9]	Dong Wen-Shan, Huang Bao-Xin.Lie symmetries and Noether conserved quantities of generalized nonholonomic mechanical systems. Acta Physica Sinica, 2010, 59(1): 1-6.doi:10.7498/aps.59.1
[10]	Lou Zhi-Mei.The extended Prelle-Singer method for the conserved quantities of second-ordinary nonlinear coupled dynamics systems and their symmetries. Acta Physica Sinica, 2010, 59(2): 719-723.doi:10.7498/aps.59.719
[11]	Zhang Yi.Birkhoff symmetries and conserved quantities of generalized Birkhoffian systems. Acta Physica Sinica, 2009, 58(11): 7436-7439.doi:10.7498/aps.58.7436
[12]	Jia Li-Qun, Cui Jin-Chao, Zhang Yao-Yu, Luo Shao-Kai.Lie symmetry and conserved quantity of Appell equation for a Chetaev’s type constrained mechanical system. Acta Physica Sinica, 2009, 58(1): 16-21.doi:10.7498/aps.58.16
[13]	Zhang Yi, Ge Wei-Kuan.Lagrange symmetries and conserved quantities for nonholonomic systems of non-Chetaev’s type. Acta Physica Sinica, 2009, 58(11): 7447-7451.doi:10.7498/aps.58.7447
[14]	Liu Yang-Kui, Fang Jian-Hui.Two types of conserved quantities of Lie-Mei symmetry for a variable mass system in phase space. Acta Physica Sinica, 2008, 57(11): 6699-6703.doi:10.7498/aps.57.6699
[15]	Zhang Kai, Wang Ce, Zhou Li-Bin.Lie symmetry and conserved quantities of Nambu mechanical systems. Acta Physica Sinica, 2008, 57(11): 6718-6721.doi:10.7498/aps.57.6718
[16]	Lou Zhi-Mei.Lagrangian function and conserved quantity of onedimensional relativistic harmonic oscillator containing a quadratic velocity drag force term. Acta Physica Sinica, 2005, 54(4): 1457-1459.doi:10.7498/aps.54.1457
[17]	Zhang Yi.Symmetries and conserved quantities of mechanical systems with unilateral holonomic constraints in phase space. Acta Physica Sinica, 2005, 54(10): 4488-4495.doi:10.7498/aps.54.4488
[18]	Fang Jian-Hui, Liao Yong-Pan, Peng Yong.Tow kinds of Mei symmeties and conserved quantities of a mechanical system in phase space. Acta Physica Sinica, 2005, 54(2): 500-503.doi:10.7498/aps.54.500
[19]	Zhang Yi.Symmetries and Mei conserved quantities for systems of generalized classical mechanics. Acta Physica Sinica, 2005, 54(7): 2980-2984.doi:10.7498/aps.54.2980
[20]	Zheng Shi-Wang, Fu Jing-Li, Li Xian-Hui.Momentum-dependent symmetries and non-Noether conserved quantities for mechanico-electrical systems. Acta Physica Sinica, 2005, 54(12): 5511-5516.doi:10.7498/aps.54.5511

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Vol. 58, Issue 9 - 2009-05-05

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