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Abstract
In this article Noether symmetry of Lagrange systems, Hamilton systems and Birkhoff systems are discussed by geometric methods. And the corresponding Noether conserved quantities are deduced.

Keywords:
dynamical systems/

geometric representation/

Noether symmetry/

Noether conserved quantity
Authors and contacts
Liu Chang¹,

Zhao Yong-Hong³,

Chen Xiang-Wei²
References

Cited By

[1]	Wang Fei-Fei, Fang Jian-Hui, Wang Ying-Li, Xu Rui-Li.Noether symmetry and Mei symmetry of a discrete holonomic mechanical system with variable mass. Acta Physica Sinica, 2014, 63(17): 170202.doi:10.7498/aps.63.170202
[2]	Zhang Yi, Jin Shi-Xin.Noether symmetries of dynamics for non-conservative systems with time delay. Acta Physica Sinica, 2013, 62(23): 234502.doi:10.7498/aps.62.234502
[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]	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]	Gu Shu-Long, Zhang Hong-Bin.Noether symmetry and the Hojman conserved quantity of the Kepler equation. Acta Physica Sinica, 2010, 59(2): 716-718.doi:10.7498/aps.59.716
[6]	Cui Jian-Xin, Gao Hai-Bo, Hong Wen-Xue.Mei symmetries and the Noether conserved quantities of super-thin elastic rod. Acta Physica Sinica, 2009, 58(11): 7426-7430.doi:10.7498/aps.58.7426
[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]	Zhang Yi.Noether’s theory for Birkhoffian systems in the event space. Acta Physica Sinica, 2008, 57(5): 2643-2648.doi:10.7498/aps.57.2643
[9]	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
[10]	Wu Hui-Bin, Mei Feng-Xiang.Two comprehensions on Noether symmetry. Acta Physica Sinica, 2006, 55(8): 3825-3828.doi:10.7498/aps.55.3825
[11]	Gu Shu-Long, Zhang Hong-Bin.Mei symmetry, Noether symmetry and Lie symmetry of an Emden system. Acta Physica Sinica, 2006, 55(11): 5594-5597.doi:10.7498/aps.55.5594
[12]	Fang Jian-Hui, Ding Ning, Wang Peng.Noether-Lie symmetry of non-holonomic mechanical system. Acta Physica Sinica, 2006, 55(8): 3817-3820.doi:10.7498/aps.55.3817
[13]	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
[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, Mei Feng-Xiang.Effects of non-conservative forces and nonholonomic constraints on Noether symmetries of a Lagrange system. Acta Physica Sinica, 2004, 53(3): 661-668.doi:10.7498/aps.53.661
[16]	Zhang Yi, Mei Feng-Xiang.Effects of constraints on Noether symmetries and conserved quantities in a Birkhoffian system. Acta Physica Sinica, 2004, 53(8): 2419-2423.doi:10.7498/aps.53.2419
[17]	Luo Shao-Kai, Guo Yong-Xin, Mei Feng-Xiang.Noether symmetry and Hojman conserved quantity for nonholonomic mechanical systems. Acta Physica Sinica, 2004, 53(5): 1270-1275.doi:10.7498/aps.53.1270
[18]	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
[19]	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
[20]	Ge Wei-Kuan.. Acta Physica Sinica, 2002, 51(5): 939-942.doi:10.7498/aps.51.939

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Vol. 59, Issue 1 - 2010-01-05

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