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用扩展Prelle-Singer法（扩展P-S法）求三自由度二阶非线性耦合动力学系统的守恒量，得到了6个积分乘子满足的确定方程、约束方程和守恒量的一般形式，并讨论了确定积分乘子的方法.最后,用扩展P-S法求得了三质点Tada晶格问题的两个守恒量.
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关键词:
- 扩展Prelle-Singer法 /
- 三自由度非线性耦合动力学系统 /
- 守恒量
In this paper, the extended Prelle-Singer (P-S) method is employed to finding the conserved quantities of three-dimensional second-order nonlinear coupled dynamic systems, the determining equations, the constraint equations of integral factors and the general expression of conserved quantities are obtained. The calculation method of integral factors is disscussed. Finally, two conserved quantities of three-particles Tada crystal lattice problem are found by extended P-S method.-
Keywords:
- extended Prelle-Singer method /
- three-dimensional nonlinear coupled dynamics systems /
- conserved quantity
[1] ［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] ［2］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）］
[3] ［3］Fang J H, Liu Y K, Zhang X N 2008 Chin. Phys. 17 1962
[4] ［4］Fu J L, Chen L Q, Chen X W 2006 Chin. Phys. 15 8
[5] ［5］Luo S K 2004 Acta Phys. Sin. 53 5（in Chinese） ［罗绍凯 2004 53 5］
[6] ［6］Lou Z M 2006 Chin. Phys. 15 891
[7] ［7］Lin P, Fang J F, Pang T 2008 Chin. Phys. 17 4361
[8] ［8］Jia L Q, Xie J F, Luo S K 2008 Chin. Phys. 17 1560
[9] ［9］Fang J H, Ding N, Wang P 2007 Chin. Phys. 16 887
[10] ］Ge W K 2008 Acta Phys. Sin. 57 6714 （in Chinese）［葛伟宽 2007 56 6714］
[11] ］Haas F, Goedert J 1996 J. Phys. A 29 4083
[12] ］Lou Z M 2005 Acta Phys. Sin. 54 1460 （in Chinese）［楼智美 2005 54 1460］
[13] ］Lou Z M 2005 Acta Phys. Sin. 54 1969（in Chinese）［楼智美 2005 54 1969］
[14] ］Kaushal R S, Gupta S 2001 J. Phys. A 34 9879
[15] ］Kaushal R S, Parashar D, Gupta S 1997 Ann. Phys. 259 233
[16] ］Lou Z M 2007 Chin. Phys. 16 1182
[17] ］Lou Z M 2007 Acta Phys. Sin. 56 2475 （in Chinese）［楼智美 2007 56 2475］
[18] ］Annamalai A, Tamizhmani K M 1994 Nonlin. Math. Phys. 1 309
[19] ］Shang M, Mei F X 2005 Chin. Phys. 14 1707
[20] ］Lou Z M, Wang W L 2006 Chin. Phys. 15 895
[21] ］Ge W K, Mei F X 2001 Acta Armam. 22 241 （in Chinese）［葛伟宽、梅凤翔 2001 兵工学报 22 241］
[22] ］Mei F X, Xie J F, Gang T Q 2007 Acta Phys. Sin. 56 5041 （in Chinese）［梅凤翔、解加芳、冮铁强 2007 56 5041］
[23] ］Prelle M J, Singer M F 1983 Trans. Amer. Math. Soc. 279 215
[24] ］Guha P, Choudhury A G, Khanra B 2009 J. Phys. A 42 115206
[25] ］Duarte L G S, Duarte S E S, da Mota L A C P, Skea J E F 2001 J. Phys. A 34 3015
[26] ］Chandrasekar V K, Senthilvelan M, Lakshmanan M 2006 J. Phys. A 39 L69
[27] ］Chandrasekar V K, Senthilvelan M, Lakshmanan M 2005 J. Nonlin. Math. Phys. 12 184
[28] ］Chandrasekar V K, Senthilvelan M, Lakshmanan M 2006 J. Math. Phys. 47 023508
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[1] ［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] ［2］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）］
[3] ［3］Fang J H, Liu Y K, Zhang X N 2008 Chin. Phys. 17 1962
[4] ［4］Fu J L, Chen L Q, Chen X W 2006 Chin. Phys. 15 8
[5] ［5］Luo S K 2004 Acta Phys. Sin. 53 5（in Chinese） ［罗绍凯 2004 53 5］
[6] ［6］Lou Z M 2006 Chin. Phys. 15 891
[7] ［7］Lin P, Fang J F, Pang T 2008 Chin. Phys. 17 4361
[8] ［8］Jia L Q, Xie J F, Luo S K 2008 Chin. Phys. 17 1560
[9] ［9］Fang J H, Ding N, Wang P 2007 Chin. Phys. 16 887
[10] ］Ge W K 2008 Acta Phys. Sin. 57 6714 （in Chinese）［葛伟宽 2007 56 6714］
[11] ］Haas F, Goedert J 1996 J. Phys. A 29 4083
[12] ］Lou Z M 2005 Acta Phys. Sin. 54 1460 （in Chinese）［楼智美 2005 54 1460］
[13] ］Lou Z M 2005 Acta Phys. Sin. 54 1969（in Chinese）［楼智美 2005 54 1969］
[14] ］Kaushal R S, Gupta S 2001 J. Phys. A 34 9879
[15] ］Kaushal R S, Parashar D, Gupta S 1997 Ann. Phys. 259 233
[16] ］Lou Z M 2007 Chin. Phys. 16 1182
[17] ］Lou Z M 2007 Acta Phys. Sin. 56 2475 （in Chinese）［楼智美 2007 56 2475］
[18] ］Annamalai A, Tamizhmani K M 1994 Nonlin. Math. Phys. 1 309
[19] ］Shang M, Mei F X 2005 Chin. Phys. 14 1707
[20] ］Lou Z M, Wang W L 2006 Chin. Phys. 15 895
[21] ］Ge W K, Mei F X 2001 Acta Armam. 22 241 （in Chinese）［葛伟宽、梅凤翔 2001 兵工学报 22 241］
[22] ］Mei F X, Xie J F, Gang T Q 2007 Acta Phys. Sin. 56 5041 （in Chinese）［梅凤翔、解加芳、冮铁强 2007 56 5041］
[23] ］Prelle M J, Singer M F 1983 Trans. Amer. Math. Soc. 279 215
[24] ］Guha P, Choudhury A G, Khanra B 2009 J. Phys. A 42 115206
[25] ］Duarte L G S, Duarte S E S, da Mota L A C P, Skea J E F 2001 J. Phys. A 34 3015
[26] ］Chandrasekar V K, Senthilvelan M, Lakshmanan M 2006 J. Phys. A 39 L69
[27] ］Chandrasekar V K, Senthilvelan M, Lakshmanan M 2005 J. Nonlin. Math. Phys. 12 184
[28] ］Chandrasekar V K, Senthilvelan M, Lakshmanan M 2006 J. Math. Phys. 47 023508
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