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含时滞的非保守系统动力学的Noether对称性

张毅 金世欣

含时滞的非保守系统动力学的Noether对称性

张毅, 金世欣
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  • 提出并研究含时滞的非保守系统动力学的Noether对称性与守恒量. 首先,建立含时滞的非保守系统的Hamilton原理,得到含时滞的Lagrange方程;其次,基于含时滞的Hamilton作用量在依赖于广义速度的无限小群变换下的不变性,定义系统的Noether对称变换和准对称变换,建立Noether对称性的判据;最后,研究对称性与守恒量之间的关系,建立含时滞的非保守系统的Noether理论. 文末举例说明结果的应用.
    • 基金项目: 国家自然科学基金(批准号:10972151,11272227)资助的课题.
    [1]

    Hu H Y, Wang Z H 1999 Adv. Mech. 29 501 (in Chinese) [胡海岩, 王在华 1999 力学进展 29 501]

    [2]

    Xu J, Pei L J 2006 Adv. Mech. 36 17 (in Chinese) [徐鉴, 裴利军 2006 力学进展 36 17]

    [3]

    Wang Z H, Hu H Y 2013 Adv. Mech. 43 3 (in Chinese) [王在华, 胡海岩 2013 力学进展 43 3]

    [4]

    Djukić Dj S, Vujanović B 1975 Acta Mech. 23 17

    [5]

    Li Z P 1981 Acta Phys. Sin. 30 1699 (in Chinese) [李子平 1981 物理学报 30 1699]

    [6]

    Bahar L Y, Kwatny H G 1987 Int. J. Non-Linear Mech. 22 125

    [7]

    Mei F X 2001 Int. J. Non-Linear Mech. 36 817

    [8]

    Xu X J, Mei F X 2005 Chin. Phys. 14 449

    [9]

    Luo S K 2007 Chin. Phys. Lett. 24 3017

    [10]

    Fu J L, Chen B Y, Chen L Q 2009 Phys. Lett. A 373 409

    [11]

    Zhang Y, Zhou Y 2013 Nonlinear Dyn. 73 783

    [12]

    Bluman G W, Anco S C 2002 Symmety and Integration Methods for Differential Equations (New York: Springer-Verlag)

    [13]

    Lutzky M 1979 J. Phys. A: Math. Gen. 12 973

    [14]

    Hojman S A 1992 J. Phys. A: Math. Gen. 25 L291

    [15]

    Wang P, Wang X M, Fang J H 2009 Chin. Phys. Lett. 26 034501

    [16]

    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)]

    [17]

    Zhang Y 2002 Acta Phys. Sin. 51 461 (in Chinese) [张毅 2002 物理学报 51 461]

    [18]

    Long Z X, Zhang Y 2013 Acta Mech. Doi: 10.1007/s00707-013-0956-5

    [19]

    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)]

    [20]

    Hojman S 1984 J. Phys. A: Math. Gen. 17 2399

    [21]

    Mei F X, Wu H B 2008 Phys. Lett. A 372 2141

    [22]

    Zhang Y 2011 Chin. Phys. B 20 034502

    [23]

    El’sgol’c L E 1964 Qualitative Methods in Mathematical Analysis (Providence: American Mathematical Society)

    [24]

    Hughes D K 1968 J. Optim. Theory Appl. 2 1

    [25]

    Palm W J, Schmitendorf W E 1974 J. Optim. Theory Appl. 14 599

    [26]

    Rosenblueth J F 1988 IMA J. Math. Control Inform. 5 125

    [27]

    Chan W L, Yung S P 1993 J. Optim. Theory Appl. 76 131

    [28]

    Lee C H, Yung S P 1996 J. Optim. Theory Appl. 88 157

    [29]

    Frederico G S F, Torres D F M 2012 Control Optim. 2 619

    [30]

    Mei F X, Wu H B 2009 Dynamics of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press)

  • [1]

    Hu H Y, Wang Z H 1999 Adv. Mech. 29 501 (in Chinese) [胡海岩, 王在华 1999 力学进展 29 501]

    [2]

    Xu J, Pei L J 2006 Adv. Mech. 36 17 (in Chinese) [徐鉴, 裴利军 2006 力学进展 36 17]

    [3]

    Wang Z H, Hu H Y 2013 Adv. Mech. 43 3 (in Chinese) [王在华, 胡海岩 2013 力学进展 43 3]

    [4]

    Djukić Dj S, Vujanović B 1975 Acta Mech. 23 17

    [5]

    Li Z P 1981 Acta Phys. Sin. 30 1699 (in Chinese) [李子平 1981 物理学报 30 1699]

    [6]

    Bahar L Y, Kwatny H G 1987 Int. J. Non-Linear Mech. 22 125

    [7]

    Mei F X 2001 Int. J. Non-Linear Mech. 36 817

    [8]

    Xu X J, Mei F X 2005 Chin. Phys. 14 449

    [9]

    Luo S K 2007 Chin. Phys. Lett. 24 3017

    [10]

    Fu J L, Chen B Y, Chen L Q 2009 Phys. Lett. A 373 409

    [11]

    Zhang Y, Zhou Y 2013 Nonlinear Dyn. 73 783

    [12]

    Bluman G W, Anco S C 2002 Symmety and Integration Methods for Differential Equations (New York: Springer-Verlag)

    [13]

    Lutzky M 1979 J. Phys. A: Math. Gen. 12 973

    [14]

    Hojman S A 1992 J. Phys. A: Math. Gen. 25 L291

    [15]

    Wang P, Wang X M, Fang J H 2009 Chin. Phys. Lett. 26 034501

    [16]

    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)]

    [17]

    Zhang Y 2002 Acta Phys. Sin. 51 461 (in Chinese) [张毅 2002 物理学报 51 461]

    [18]

    Long Z X, Zhang Y 2013 Acta Mech. Doi: 10.1007/s00707-013-0956-5

    [19]

    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)]

    [20]

    Hojman S 1984 J. Phys. A: Math. Gen. 17 2399

    [21]

    Mei F X, Wu H B 2008 Phys. Lett. A 372 2141

    [22]

    Zhang Y 2011 Chin. Phys. B 20 034502

    [23]

    El’sgol’c L E 1964 Qualitative Methods in Mathematical Analysis (Providence: American Mathematical Society)

    [24]

    Hughes D K 1968 J. Optim. Theory Appl. 2 1

    [25]

    Palm W J, Schmitendorf W E 1974 J. Optim. Theory Appl. 14 599

    [26]

    Rosenblueth J F 1988 IMA J. Math. Control Inform. 5 125

    [27]

    Chan W L, Yung S P 1993 J. Optim. Theory Appl. 76 131

    [28]

    Lee C H, Yung S P 1996 J. Optim. Theory Appl. 88 157

    [29]

    Frederico G S F, Torres D F M 2012 Control Optim. 2 619

    [30]

    Mei F X, Wu H B 2009 Dynamics of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press)

  • 引用本文:
    Citation:
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  • 文章访问数:  1494
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出版历程
  • 收稿日期:  2013-07-18
  • 修回日期:  2013-08-05
  • 刊出日期:  2013-12-05

含时滞的非保守系统动力学的Noether对称性

  • 1. 苏州科技学院土木工程学院, 苏州 215011;
  • 2. 苏州科技学院数理学院, 苏州 215009
    基金项目: 

    国家自然科学基金(批准号:10972151,11272227)资助的课题.

摘要: 提出并研究含时滞的非保守系统动力学的Noether对称性与守恒量. 首先,建立含时滞的非保守系统的Hamilton原理,得到含时滞的Lagrange方程;其次,基于含时滞的Hamilton作用量在依赖于广义速度的无限小群变换下的不变性,定义系统的Noether对称变换和准对称变换,建立Noether对称性的判据;最后,研究对称性与守恒量之间的关系,建立含时滞的非保守系统的Noether理论. 文末举例说明结果的应用.

English Abstract

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