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三自由度二阶非线性耦合动力学系统守恒量的扩展Prelle-Singer求法

楼智美

三自由度二阶非线性耦合动力学系统守恒量的扩展Prelle-Singer求法

楼智美
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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.
    [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

  • [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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出版历程
  • 收稿日期:  2009-08-14
  • 修回日期:  2009-09-08
  • 刊出日期:  2010-03-05

三自由度二阶非线性耦合动力学系统守恒量的扩展Prelle-Singer求法

  • 1. 绍兴文理学院物理系,绍兴 312000

摘要: 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.

English Abstract

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