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Abstract
For a generalized Hamiltonian system, a new conservation law derived by using the Lie symmetry is studies. Firstly, the differential equations of the system are given. Secondly, the Lie symmetry under special infinitesimal transformations is studied. Thirdly, the theorem of Hojman is generalized to this system. Finally, an example is given to illustrate the application of the result.

Keywords:
generalized Hamiltonian system/

Lie symmetry/

conserved quantity
Authors and contacts
Mei Feng-Xiang

1.
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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]	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
[5]	Jiang Wen-An, Luo Shao-Kai.Mei symmetry leading to Mei conserved quantity of generalized Hamiltonian system. Acta Physica Sinica, 2011, 60(6): 060201.doi:10.7498/aps.60.060201
[6]	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
[7]	Shi Shen-Yang, Huang Xiao-Hong, Zhang Xiao-Bo, Jin Li.The Lie symmetry and Noether conserved quantity of discrete difference variational Hamilton system. Acta Physica Sinica, 2009, 58(6): 3625-3631.doi:10.7498/aps.58.3625
[8]	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
[9]	Liu Chang, Liu Shi-Xing, Mei Feng-Xiang, Guo Yong-Xin.Conformal invariance and Hojman conserved quantities of generalized Hamilton systems. Acta Physica Sinica, 2008, 57(11): 6709-6713.doi:10.7498/aps.57.6709
[10]	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
[11]	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
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[13]	Zhang Peng-Yu, Fang Jian-Hui.Lie symmetry and non-Noether conserved quantities of variable mass Birkhoffian system. Acta Physica Sinica, 2006, 55(8): 3813-3816.doi:10.7498/aps.55.3813
[14]	Gu Shu-Long, Zhang Hong-Bin.Mei symmetry, Noether symmetry and Lie symmetry of a Vacco system. Acta Physica Sinica, 2005, 54(9): 3983-3986.doi:10.7498/aps.54.3983
[15]	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
[16]	Luo Shao-Kai.Mei symmetry, Noether symmetry and Lie symmetry of Hamiltonian system. Acta Physica Sinica, 2003, 52(12): 2941-2944.doi:10.7498/aps.52.2941
[17]	Li Yuan-Cheng, Zhang Yi, Liang Jing-Hui.. Acta Physica Sinica, 2002, 51(10): 2186-2190.doi:10.7498/aps.51.2186
[18]	ZHANG YI, XUE YUN.LIE SYMMETRIES OF CONSTRAINED HAMILTONIAN SYSTEM WITH THE SECOND TYPE OF CONSTRAINTS . Acta Physica Sinica, 2001, 50(5): 816-819.doi:10.7498/aps.50.816
[19]	MEI FENG-XIANG, SHANG MEI.LIE SYMMETRIES AND CONSERVED QUANTITIES OF FIRST ORDER LAGRANGE SYSTEMS. Acta Physica Sinica, 2000, 49(10): 1901-1903.doi:10.7498/aps.49.1901
[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 5 - 2003-03-05

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