搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

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

引用本文:
Citation:

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

Finding conserved quantities of three-dimensional second-order nonlinear coupled dynamics systems by the extended Prelle-Singer method

Lou Zhi-Mei
PDF
导出引用
  • 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.
    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.
    [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

  • [1] 郑世旺, 王建波, 陈向炜, 李彦敏, 解加芳. 变质量非完整系统Tznoff方程的Lie 对称性与其导出的守恒量. 物理学报, 2012, 61(11): 111101. doi: 10.7498/aps.61.111101
    [2] 张斌, 方建会, 张克军. 变质量非完整系统的Lagrange对称性与守恒量. 物理学报, 2012, 61(2): 021101. doi: 10.7498/aps.61.021101
    [3] 楼智美, 梅凤翔. 二维各向异性谐振子的第三个独立守恒量及其对称性. 物理学报, 2012, 61(11): 110201. doi: 10.7498/aps.61.110201
    [4] 薛纭, 王鹏. Cosserat弹性杆动力学普遍定理的守恒量问题. 物理学报, 2011, 60(11): 114501. doi: 10.7498/aps.60.114501
    [5] 李元成, 夏丽莉, 王小明, 刘晓巍. 完整系统Appell方程的Lie-Mei对称性与守恒量. 物理学报, 2010, 59(6): 3639-3642. doi: 10.7498/aps.59.3639
    [6] 李元成, 王小明, 夏丽莉. 完整系统Nielsen方程的统一对称性与守恒量. 物理学报, 2010, 59(5): 2935-2938. doi: 10.7498/aps.59.2935
    [7] 楼智美. 二阶非线性耦合动力学系统守恒量的扩展Prelle-Singer求法与对称性研究. 物理学报, 2010, 59(2): 719-723. doi: 10.7498/aps.59.719
    [8] 陈向炜, 赵永红, 刘畅. 变质量完整动力学系统的共形不变性与守恒量. 物理学报, 2009, 58(8): 5150-5154. doi: 10.7498/aps.58.5150
    [9] 张毅. 广义Birkhoff系统的Birkhoff对称性与守恒量. 物理学报, 2009, 58(11): 7436-7439. doi: 10.7498/aps.58.7436
    [10] 蔡建乐, 梅凤翔. Lagrange系统Lie点变换下的共形不变性与守恒量. 物理学报, 2008, 57(9): 5369-5373. doi: 10.7498/aps.57.5369
    [11] 葛伟宽. 一类完整系统的Mei对称性与守恒量. 物理学报, 2008, 57(11): 6714-6717. doi: 10.7498/aps.57.6714
    [12] 郑世旺, 贾利群. 非完整系统Tzénoff方程的Mei对称性和守恒量. 物理学报, 2007, 56(2): 661-665. doi: 10.7498/aps.56.661
    [13] 楼智美. 一类多自由度线性耦合系统的对称性与守恒量研究. 物理学报, 2007, 56(5): 2475-2478. doi: 10.7498/aps.56.2475
    [14] 郑世旺, 傅景礼, 李显辉. 机电动力系统的动量依赖对称性和非Noether守恒量. 物理学报, 2005, 54(12): 5511-5516. doi: 10.7498/aps.54.5511
    [15] 张 毅. 广义经典力学系统的对称性与Mei守恒量. 物理学报, 2005, 54(7): 2980-2984. doi: 10.7498/aps.54.2980
    [16] 张 毅, 梅凤翔. 约束对Birkhoff系统Noether对称性和守恒量的影响. 物理学报, 2004, 53(8): 2419-2423. doi: 10.7498/aps.53.2419
    [17] 张 毅, 范存新, 葛伟宽. Birkhoff系统的一类新型守恒量. 物理学报, 2004, 53(11): 3644-3647. doi: 10.7498/aps.53.3644
    [18] 张毅. Birkhoff系统的一类Lie对称性守恒量. 物理学报, 2002, 51(3): 461-464. doi: 10.7498/aps.51.461
    [19] 李元成, 张毅, 梁景辉. 一类非完整奇异系统的Lie对称性与守恒量. 物理学报, 2002, 51(10): 2186-2190. doi: 10.7498/aps.51.2186
    [20] 梅凤翔. 包含伺服约束的非完整系统的Lie对称性与守恒量. 物理学报, 2000, 49(7): 1207-1210. doi: 10.7498/aps.49.1207
计量
  • 文章访问数:  7521
  • PDF下载量:  855
  • 被引次数: 0
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

/

返回文章
返回