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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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