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Lie symmetry and Hojman conserved quantity for Nielsen equations in a dynamical system of the relative motion are investigated. The definition and the criterion of Lie symmetry of Nielsen equations in a dynamical system of the relative motion under the infinitesimal transformations of groups are given. The expressions of the determining equation of Lie symmetry of Nielsen equations and Hojman conserved quantity deduced directly from Lie symmetry in a dynamical system of the relative motion are obtained. An example is given to illustrate the application of the results.
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Keywords:
- dynamics of relative motion /
- Nielsen equations /
- Lie symmetry /
- Hojman conserved quantity
[1] Noether A E 1918 Nachr. Akad. Wiss. Gttingen. Math. Phys. KI II 235
[2] Lee T D 1983 Phys.Lett.B 122 217
[3] Hojman S A1992 J.Phys.A:Math.Gen. 25 L291
[4] Lutzky M 1995 J. Phys.A:Math.Gen. 28 L637
[5] Bokhari A H,Kashif A R 1996 J. Math. Phys. 37 3496
[6] Mei F X,Liu D,Luo Y 1991 Advanced Analytical Mechanics (Beijing:Bengjing Institute of Technology Press)(in Chinese)[梅凤翔、刘 端、罗 勇 1991 高等分析力学(北京:北京理工大学出版社)]
[7] 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)]
[8] Fu J L,Wang X M 2000 Acta. Phys. Sin. 49 1023 (in Chinese) [傅景礼、王新民2000 物理学报 49 1023]
[9] Fang J H, Zhao S Q 2002 Chin. Phys. 11 445
[10] Zhang Y 2003 Acta Phys.Sin. 52 1832 (in Chinese)[张 毅 2003 物理学报 52 1832] [11] Luo S K 2004 Acta Phys.Sin. 53 5(in Chinese)[罗绍凯 2004 物理学报 53 5]
[11] Mei F X 2004 Symmetries and Conserved Quantities of Constranined Mechanical Systems (Beijing:Beijing Institute of Technology Press) (in Chinese)[梅凤翔 2004约束力学系统的对称性和守恒量(北京:北京理工大学出版社)]
[12] Xu X J,Mei F X,Zhang Y F 2006 Chin. Phys. 15 19
[13] Mei F X,Wu H B,Zhang Y F.2006 Chin. Phys. 15 1932
[14] Xia L L,Li Y C,Wang J,Hou Q B 2006 Acta Phys.Sin. 55 4995(in Chinese)[夏丽莉、李元成、王 静、后其宝2006 物理学报 55 4995]
[15] Shang M,Guo Y X,Mei F X 2007 Chin.Phys . 16 292
[16] Shi S Y, Fu J L, Chen L Q 2007 Acta. Phys. Sim. 56 3060 (in Chinese) [施沈阳、傅景礼、陈立群 2007 物理学报 56 3060]
[17] Ge W K 2008 Acta Phys.Sin. 57 6714 (in Chinese)[葛伟宽2008 物理学报 57 6714]
[18] Cui J C,Zhang Y Y, Jia L Q 2009 Chin.Phys.B 18 1731
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[1] Noether A E 1918 Nachr. Akad. Wiss. Gttingen. Math. Phys. KI II 235
[2] Lee T D 1983 Phys.Lett.B 122 217
[3] Hojman S A1992 J.Phys.A:Math.Gen. 25 L291
[4] Lutzky M 1995 J. Phys.A:Math.Gen. 28 L637
[5] Bokhari A H,Kashif A R 1996 J. Math. Phys. 37 3496
[6] Mei F X,Liu D,Luo Y 1991 Advanced Analytical Mechanics (Beijing:Bengjing Institute of Technology Press)(in Chinese)[梅凤翔、刘 端、罗 勇 1991 高等分析力学(北京:北京理工大学出版社)]
[7] 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)]
[8] Fu J L,Wang X M 2000 Acta. Phys. Sin. 49 1023 (in Chinese) [傅景礼、王新民2000 物理学报 49 1023]
[9] Fang J H, Zhao S Q 2002 Chin. Phys. 11 445
[10] Zhang Y 2003 Acta Phys.Sin. 52 1832 (in Chinese)[张 毅 2003 物理学报 52 1832] [11] Luo S K 2004 Acta Phys.Sin. 53 5(in Chinese)[罗绍凯 2004 物理学报 53 5]
[11] Mei F X 2004 Symmetries and Conserved Quantities of Constranined Mechanical Systems (Beijing:Beijing Institute of Technology Press) (in Chinese)[梅凤翔 2004约束力学系统的对称性和守恒量(北京:北京理工大学出版社)]
[12] Xu X J,Mei F X,Zhang Y F 2006 Chin. Phys. 15 19
[13] Mei F X,Wu H B,Zhang Y F.2006 Chin. Phys. 15 1932
[14] Xia L L,Li Y C,Wang J,Hou Q B 2006 Acta Phys.Sin. 55 4995(in Chinese)[夏丽莉、李元成、王 静、后其宝2006 物理学报 55 4995]
[15] Shang M,Guo Y X,Mei F X 2007 Chin.Phys . 16 292
[16] Shi S Y, Fu J L, Chen L Q 2007 Acta. Phys. Sim. 56 3060 (in Chinese) [施沈阳、傅景礼、陈立群 2007 物理学报 56 3060]
[17] Ge W K 2008 Acta Phys.Sin. 57 6714 (in Chinese)[葛伟宽2008 物理学报 57 6714]
[18] Cui J C,Zhang Y Y, Jia L Q 2009 Chin.Phys.B 18 1731
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