Mei symmetry, Noether symmetry and Lie symmetry of Hamiltonian system

Luo Shao-Kai

doi:10.7498/aps.52.2941

Abstract
The Mei symmetry, i.e. the form invariance, of a Hamiltonian system is studied. The definition and the determining equation of Mei symmetry in the Hamiltonian system are given. The relations among the Mei symmetry, the Noether symmetry and the Lie symmetry are studied, and the conserved quantities of Hamiltonian system are obtained. An example is given to illustrate the application of the result.

Keywords:
Hamiltonian system /

Mei symmetry /

Noether symmetry /

Lie symmetry /

conserved quatntity
Authors and contacts
Luo Shao-Kai

1.
长沙大学数学力学与数学物理研究所，长沙 410003
References

Cited By

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[2]	Lou Zhi-Mei. The study of conserved quantities and symmetries for two-dimensional isotropic harmonic charged oscillator moving in homogeneous magnetic field. Acta Physica Sinica, 2013, 62(22): 220201. doi: 10.7498/aps.62.220201
[3]	Xu Rui-Li, Fang Jian-Hui, Zhang Bin. The Noether conserved quantity of Lie symmetry for discrete difference sequence Hamilton system with variable mass. Acta Physica Sinica, 2013, 62(15): 154501. doi: 10.7498/aps.62.154501
[4]	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
[5]	Cai Jian-Le. Conformal invariance and conserved quantities of Mei symmetry for general holonomic systems. Acta Physica Sinica, 2009, 58(1): 22-27. doi: 10.7498/aps.58.22
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[7]	Ge Wei-Kuan. Mei symmetry and conserved quantity of a holonomic system. Acta Physica Sinica, 2008, 57(11): 6714-6717. doi: 10.7498/aps.57.6714
[8]	Lou Zhi-Mei. The study of symmetries and conserved quantities for one-dimensional damped-amplified harmonic oscillators. Acta Physica Sinica, 2008, 57(3): 1307-1310. doi: 10.7498/aps.57.1307
[9]	Zheng Shi-Wang, Jia Li-Qun. Mei symmetry and conserved quantity of Tzénoff equations for nonholonomic systems. Acta Physica Sinica, 2007, 56(2): 661-665. doi: 10.7498/aps.56.661
[10]	Fang Jian-Hui, Ding Ning, Wang Peng. A new type of conserved quantity of Mei symmetry for Hamilton system. Acta Physica Sinica, 2007, 56(6): 3039-3042. doi: 10.7498/aps.56.3039
[11]	Lou Zhi_Mei. The study of symmetries and conserved quantities for one class of linearly coupled multidimensional freedom systems. Acta Physica Sinica, 2007, 56(5): 2475-2478. doi: 10.7498/aps.56.2475
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[13]	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
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[16]	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
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[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
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[20]	MEI FENG-XIANG. LIE SYMMETRIES AND CONSERVED QUANTITIES OF NONHOLONOMIC SYSTEMS WITH SERVOCONSTR AINTS. Acta Physica Sinica, 2000, 49(7): 1207-1210. doi: 10.7498/aps.49.1207

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Vol. 52, Issue 12 - 2003-06-20

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Mei symmetry, Noether symmetry and Lie symmetry of Hamiltonian system

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Mei symmetry, Noether symmetry and Lie symmetry of Hamiltonian system

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