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We obtained the orbit differential equation of Kepler system when the θ is the independent variable. The Lie symmetries and invariants of the orbit differential equation for Kepler system , the exact Lie symmetries and exact invariants of the orbit differential equation for perturbed Kepler system are discussed firstly. Then we discuss the approximate Lie symmetries and approximate invariants of the orbit differential equation for perturbed Kepler system. Nine first order approximate Lie symmetries and six first order approximate invariants are obtained, one of them is a exact invariant in fact, and the other five of them are equivalent to the corresponding invariants of Kepler system multiplyied by the perturbation coefficient ε.
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Keywords:
- orbit differential equation for perturbed Kepler system /
- approximate Lie symmetries /
- approximate invariants
[1] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) (in Chinese) [梅凤翔 1999 李群和李代数对约束力学系统的应用(北京:科学出版社)]
[2] Zhao Y Y,Mei F X 1999 Symmetries and Invariants of Mechanical System (Beijing: Science Press) (in Chinese) [赵跃宇、梅凤翔 1999 力学系统的对称性与不变量(北京:科学出版社)]
[3] Lou Z M 2006 Chin. Phys. 15 891
[4] Fu J L, Chen L Q,Chen X W 2006 Chin. Phys. 15 8
[5] Jia L Q , Xie J F,Luo S K 2008 Chin. Phys. B 17 1560
[6] Fang J H 2009 Acta Phys. Sin. 58 3617 (in Chinese)[方建会 2009 物理学报 58 3617]
[7] Jia L Q, Cui J C, Zhang Y Y, Luo S K 2009 Acta Phys. Sin. 58 16 (in Chinese)[贾利群、崔金超、张耀宇、罗绍凯 2009物理 学报 58 16] 〖8] Zhao L,Fu J L,Chen B Y 2010 Chin. Phys. B 19 010301
[8] Govinder K S, Heil T G,Uzer T 1998 Phys. Lett. A 240 127
[9] Leach P G L, Moyo S, Cotsakis S,Lemmer R L 2001 J. Nonlinear Math. Phys. 1 139
[10] Kara A H, Mahomed F M,Unal G 1999 Int. J. Theoret. Phys. 38 2389
[11] Unal G 2001 Nonlinear Dyn. 26 309
[12] Unal G, Gorali G 2002 Nonlinear Dyn. 28 195
[13] Feroze T, Kara A H 2002 Int. J. Non-linear Mech. 37 275
[14] Ibragimov N H, Unal G, Jogreus C 2004 J Math. Anal. Appl. 297 152
[15] Dolapci I T, Pakdemirli M 2004 Int. J. Non-linear Mech. 39 1603
[16] Kara A H, Mahomed F M, Qadir A 2008 Nonlinear Dyn. 51 183
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[1] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) (in Chinese) [梅凤翔 1999 李群和李代数对约束力学系统的应用(北京:科学出版社)]
[2] Zhao Y Y,Mei F X 1999 Symmetries and Invariants of Mechanical System (Beijing: Science Press) (in Chinese) [赵跃宇、梅凤翔 1999 力学系统的对称性与不变量(北京:科学出版社)]
[3] Lou Z M 2006 Chin. Phys. 15 891
[4] Fu J L, Chen L Q,Chen X W 2006 Chin. Phys. 15 8
[5] Jia L Q , Xie J F,Luo S K 2008 Chin. Phys. B 17 1560
[6] Fang J H 2009 Acta Phys. Sin. 58 3617 (in Chinese)[方建会 2009 物理学报 58 3617]
[7] Jia L Q, Cui J C, Zhang Y Y, Luo S K 2009 Acta Phys. Sin. 58 16 (in Chinese)[贾利群、崔金超、张耀宇、罗绍凯 2009物理 学报 58 16] 〖8] Zhao L,Fu J L,Chen B Y 2010 Chin. Phys. B 19 010301
[8] Govinder K S, Heil T G,Uzer T 1998 Phys. Lett. A 240 127
[9] Leach P G L, Moyo S, Cotsakis S,Lemmer R L 2001 J. Nonlinear Math. Phys. 1 139
[10] Kara A H, Mahomed F M,Unal G 1999 Int. J. Theoret. Phys. 38 2389
[11] Unal G 2001 Nonlinear Dyn. 26 309
[12] Unal G, Gorali G 2002 Nonlinear Dyn. 28 195
[13] Feroze T, Kara A H 2002 Int. J. Non-linear Mech. 37 275
[14] Ibragimov N H, Unal G, Jogreus C 2004 J Math. Anal. Appl. 297 152
[15] Dolapci I T, Pakdemirli M 2004 Int. J. Non-linear Mech. 39 1603
[16] Kara A H, Mahomed F M, Qadir A 2008 Nonlinear Dyn. 51 183
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