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Abstract
The Noether symmetry and the Hojman conserved quantities of the Kepler equation are studied. The determining equations of Noether symmetry for the system are given. A theorem asserting that the Noether symmetry for the system leads to the Hojman conserved quantity is presented.

Keywords:
Kepler equation/

Noether symmetry/

Hojman conserved quantity
Authors and contacts
Gu Shu-Long²,

Zhang Hong-Bin¹
References

Cited By

[1]	Sun Xian-Ting, Zhang Yao-Yu, Zhang Fang, Jia Li-Qun.Conformal invariance and Hojman conserved quantity of Lie symmetry for Appell equations in a holonomic system. Acta Physica Sinica, 2014, 63(14): 140201.doi:10.7498/aps.63.140201
[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]	Liu Hong-Wei, Li Ling-Fei, Yang Shi-Tong.Conformal invariance, Mei symmetry and the conserved quantity of the Kepler equation. Acta Physica Sinica, 2012, 61(20): 200202.doi:10.7498/aps.61.200202
[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]	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
[6]	Liu Chang, Mei Feng-Xiang, Guo Yong-Xin.Conformal symmetry and Hojman conserved quantity of Lagrange system. Acta Physica Sinica, 2008, 57(11): 6704-6708.doi:10.7498/aps.57.6704
[7]	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
[8]	Jia Li-Qun, Zhang Yao-Yu, Zheng Shi-Wang.Hojman conserved quantities for systems with non-Chetaev nonholonomic constraints in the event space. Acta Physica Sinica, 2007, 56(2): 649-654.doi:10.7498/aps.56.649
[9]	Ge Wei-Kuan.Mei symmetries of a type of dynamical equations. Acta Physica Sinica, 2007, 56(1): 1-4.doi:10.7498/aps.56.1
[10]	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
[11]	Hu Chu-Le, Xie Jia-Fang.Form invariance and Hojman conserved quantity of Maggi equation. Acta Physica Sinica, 2007, 56(9): 5045-5048.doi:10.7498/aps.56.5045
[12]	Zhang Yi.Non-Noether conserved quantities for systems with unilateral non-Chetaev nonholonomic constraints. Acta Physica Sinica, 2006, 55(2): 504-510.doi:10.7498/aps.55.504
[13]	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
[14]	Xu Xue-Jun, Mei Feng-Xiang, Qin Mao-Chang.Hojman conserved quantity for a holonomic system in the event space. Acta Physica Sinica, 2005, 54(3): 1009-1014.doi:10.7498/aps.54.1009
[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]	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
[17]	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
[18]	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
[19]	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
[20]	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

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Vol. 59, Issue 2 - 2010-01-20

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