Conformal invariance, Mei symmetry and the conserved quantity of the Kepler equation

Liu Hong-Wei; Li Ling-Fei; Yang Shi-Tong

doi:10.7498/aps.61.200202

Abstract

In this paper, the conformal invariance and Mei symmetry of Kepler system under infinitesimal transformations are discussed in detail. The new conserved quantity of the system is given, which is different from the total energy and the angular momentum. The independences of these conserved quantities are discussed in the space which is composed of general ordinates and general speed.

Keywords:

Authors and contacts

1.
Institute of Mathematics, Jilin University, Changchun 130012, China;
2.
School of Sciences, Northeast Dianli University, Jilin 132012, China

References

[1]	Noether A E 1918 Nachr. Akad. Wiss. Gottingen: Math. Phys. 2 235
[2]	Hojman S A 1992 J. Phys. A: Math. Gen. 25 L291
[3]	Mei F X 2000 J. Beijing Inst. Technol. 9 120
[4]	Fang J H 2003 Commun. Theor. Phys. 40 269
[5]	Luo S K 2003 Acta Phys. Sin. 52 2941 (in Chinese) [罗绍凯 2003 52 2941]
[6]	Gu S L, Zhang H B 2010 Acta Phys. Sin. 59 716 (in Chinese) [顾书龙, 张宏彬 2010 59 716]
[7]	Gu S L, Zhang H B 2009 J. Chongqing Inst. Technol. (Natural Science) 23 39 (in Chinese) [顾书龙, 张宏彬 2009 重庆工学院学报(自然科学) 23 39]
[8]	Chen X W, Li Y M, Zhao Y H 2005 Phys. Lett. A 337 274
[9]	Cai J L, Mei F X 2008 Acta Phys. Sin. 57 5369 (in Chinese) [蔡建乐, 梅凤翔 2008 57 5369]
[10]	Liu C, Mei F X, Guo Y X 2008 Acta Phys. Sin. 57 6704 (in Chinese) [刘畅, 梅凤翔, 郭永新 2008 57 6704]
[11]	Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 2004 约束力学系统的对称性与守恒量(北京:北京理工大学出版社)]
[12]	Jia L Q, Zhang Y Y, Yang X F, Cui J C, Xie Y L 2010 Acta Phys. Sin. 59 2939 (in Chinese) [贾利群, 张耀宇, 杨新芳, 崔金超, 解银丽 2010 59 2939]
[13]	Mei F X 2002 Chin. Sci. Bull. 47 1544

Cited By

[1]	Noether A E 1918 Nachr. Akad. Wiss. Gottingen: Math. Phys. 2 235
[2]	Hojman S A 1992 J. Phys. A: Math. Gen. 25 L291
[3]	Mei F X 2000 J. Beijing Inst. Technol. 9 120
[4]	Fang J H 2003 Commun. Theor. Phys. 40 269
[5]	Luo S K 2003 Acta Phys. Sin. 52 2941 (in Chinese) [罗绍凯 2003 52 2941]
[6]	Gu S L, Zhang H B 2010 Acta Phys. Sin. 59 716 (in Chinese) [顾书龙, 张宏彬 2010 59 716]
[7]	Gu S L, Zhang H B 2009 J. Chongqing Inst. Technol. (Natural Science) 23 39 (in Chinese) [顾书龙, 张宏彬 2009 重庆工学院学报(自然科学) 23 39]
[8]	Chen X W, Li Y M, Zhao Y H 2005 Phys. Lett. A 337 274
[9]	Cai J L, Mei F X 2008 Acta Phys. Sin. 57 5369 (in Chinese) [蔡建乐, 梅凤翔 2008 57 5369]
[10]	Liu C, Mei F X, Guo Y X 2008 Acta Phys. Sin. 57 6704 (in Chinese) [刘畅, 梅凤翔, 郭永新 2008 57 6704]
[11]	Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 2004 约束力学系统的对称性与守恒量(北京:北京理工大学出版社)]
[12]	Jia L Q, Zhang Y Y, Yang X F, Cui J C, Xie Y L 2010 Acta Phys. Sin. 59 2939 (in Chinese) [贾利群, 张耀宇, 杨新芳, 崔金超, 解银丽 2010 59 2939]
[13]	Mei F X 2002 Chin. Sci. Bull. 47 1544

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Vol. 61, Issue 20 - 2012-10-20

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Conformal invariance, Mei symmetry and the conserved quantity of the Kepler equation

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Conformal invariance, Mei symmetry and the conserved quantity of the Kepler equation

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