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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
[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物理学报 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物理学报 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 物理学报 54 1460］
[13] ］Lou Z M 2005 Acta Phys. Sin. 54 1969（in Chinese）［楼智美 2005 物理学报 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 物理学报 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 物理学报 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物理学报 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物理学报 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 物理学报 54 1460］
[13] ］Lou Z M 2005 Acta Phys. Sin. 54 1969（in Chinese）［楼智美 2005 物理学报 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 物理学报 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 物理学报 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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