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Abstract
In this paper, a new kind of symmetry and its conserved quantities of a mechanical system in the phase space are studied. The definition of this new symmetry, i.e., the Lie-Mei symmetry is presented, and the criterion of this new symmetry is also given. The generalized Hojman and the Mei conserved quantities of the Lie-Mei symmetry of the system are obtained. An example is given to illustrative the application of the result.

Keywords:
phase space/

mechanical system/

Lie-Mei symmetry/

conserved quantity
Authors and contacts
Fang Jian-Hui,

Wang Peng,

Ding Ning

1.
References

Cited By

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[2]	Xu Chao, Li Yuan-Cheng.Lie-Mei symmetry and conserved quantities of Nielsen equations for a singular nonholonomic system of Chetaev'type. Acta Physica Sinica, 2013, 62(12): 120201.doi:10.7498/aps.62.120201
[3]	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
[4]	Li Yuan-Cheng, Xia Li-Li, Wang Xiao-Ming, Liu Xiao-Wei.Lie-Mei symmetry and conserved quantities of Appell equation for a holonomic mechanical system. Acta Physica Sinica, 2010, 59(6): 3639-3642.doi:10.7498/aps.59.3639
[5]	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
[6]	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
[7]	Lu Kai, Fang Jian-Hui, Zhang Ming-Jiang, Wang Peng.Noether symmetry and Mei symmetry of discrete holonomic system in phase space. Acta Physica Sinica, 2009, 58(11): 7421-7425.doi:10.7498/aps.58.7421
[8]	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
[9]	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
[10]	Zhang Yi.Perturbation of symmetries and Hojman adiabatic invariants of discrete mechanical systems in the phase space. Acta Physica Sinica, 2007, 56(4): 1855-1859.doi:10.7498/aps.56.1855
[11]	Xia Li-Li, Li Yuan-Cheng.Perturbation to symmetries and adiabatic invariant for nonholonomic controllable mechanical system in phase place. Acta Physica Sinica, 2007, 56(11): 6183-6187.doi:10.7498/aps.56.6183
[12]	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
[13]	Zhang Yi, Ge Wei-Kuan.A new conservation law from Mei symmetry for the relativistic mechanical system. Acta Physica Sinica, 2005, 54(4): 1464-1467.doi:10.7498/aps.54.1464
[14]	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
[15]	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
[16]	Fang Jian－Hui, Zhang Peng－Yu.The conserved quantity of Hojman for mechanicalsystems with variable mass in phase space. Acta Physica Sinica, 2004, 53(12): 4041-4044.doi:10.7498/aps.53.4041
[17]	Lou Zhi-Mei.Form invariance of second-order linear nonholonomic systems in phase space. Acta Physica Sinica, 2004, 53(7): 2046-2049.doi:10.7498/aps.53.2046
[18]	Mei Feng-Xiang.Lie symmetry and the conserved quantity of a generalized Hamiltonian system. Acta Physica Sinica, 2003, 52(5): 1048-1050.doi:10.7498/aps.52.1048
[19]	Fang Jian-Hui, Yan Xiang-Hong, Chen Pei-Sheng.Form invariance and Noether symmetry of a relativistic mechanical system. Acta Physica Sinica, 2003, 52(7): 1561-1564.doi:10.7498/aps.52.1561
[20]	Fang Jian-Hui, Chen Pei-Sheng, Zhang Jun, Li Hong.Form invariance and Lie symmetry of relativistic mechanical system. Acta Physica Sinica, 2003, 52(12): 2945-2948.doi:10.7498/aps.52.2945

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Vol. 55, Issue 8 - 2006-04-20

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