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力学系统的二阶梯度表示

楼智美 梅凤翔

引用本文:
Citation:

力学系统的二阶梯度表示

楼智美, 梅凤翔

A second order gradient representation of mechanics system

Lou Zhi-Mei, Mei Feng-Xiang
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  • 研究力学系统运动微分方程的梯度表示以及二阶梯度表示. 将完整和非完整力学系统的微分方程在正则坐标下表出. 给出系统成为梯度系统以及二阶梯度系统的条件. 举例说明结果的应用.
    A gradient representation and a second order gradient representation of the mechanics system are studied. The differential equations of motion of the holonomic and nonholonomic mechanics systems are expressed in the canonical coordinates. A condition under which the system can be considered as a gradient system is given. A condition under which the system can be considered as a second order gradient system is obtained. Two examples are given to illustrate the application of the result.
    • 基金项目: 国家自然科学基金重点项目;(批准号: 10932002)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 10932002).
    [1]

    Tarasov V E 2010 Fractional Dynamics (Beijing: Higher Education Press)

    [2]

    Zhou S, Fu J L, Liu Y S 2010 Chin. Phys. B 20 120301

    [3]

    Novoselov V S 1966 Variational Methods in Mechanics (Leningrad: L G V Press) (in Russian)

    [4]

    Mei F X 1985 Foundations of Mechanics of Nonholonomic systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 1985 非完整系统力学基础(北京:北京工业学院出版社)]

    [5]

    Mei F X 2000 Appl. Mech. Rev. 53 283

    [6]

    Lou Z M 2006 Chin. Phys. 15 891

    [7]

    Zhang H B 2002 Chin. Phys. 11 1

    [8]

    Zhang R C 2000 Chin. Phys. 9 561

    [9]

    Lou Z M 2007 Chin. Phys. 16 1182

    [10]

    Wang S Y, Mei F X 2002 Chin. Phys. 11 5

    [11]

    Wang S Y, Mei F X 2001 Chin. Phys. 10 373

    [12]

    Mei F X, Zheng G H 2002 Acta Mech. Sin. 18 414

    [13]

    Mei F X 2002 Chin. Sci. Bull. 47 2019

    [14]

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

    [15]

    Xie J F, Gang T Q, Mei F X 2008 Chin. Phys. B 17 390

    [16]

    Sarlet W, Cantrijn F 1981 J. Phys. A: Math. Gen. 14 2227

    [17]

    Hojman S A1983 J. Phys. A: Math. Gen. 16 1383

    [18]

    Bloch A M, Krishnaprasad P S, Marsden J E, Murray R M 1996 Arch. Rational Mech. Anal. 136 21

    [19]

    Kara A, Mahomed F 2000 Int. J. Theor. Phys. 39 23

    [20]

    Beksert X, Park J H 2009 Eur. Phys. J. C 61 141

    [21]

    Jiang W A, Li Z J, Lou S K 2011 Chin. Phys. B 20 030202

    [22]

    Dong W S, Huang B X, Fang J H 2011 Chin. Phys. B 20 010204

  • [1]

    Tarasov V E 2010 Fractional Dynamics (Beijing: Higher Education Press)

    [2]

    Zhou S, Fu J L, Liu Y S 2010 Chin. Phys. B 20 120301

    [3]

    Novoselov V S 1966 Variational Methods in Mechanics (Leningrad: L G V Press) (in Russian)

    [4]

    Mei F X 1985 Foundations of Mechanics of Nonholonomic systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 1985 非完整系统力学基础(北京:北京工业学院出版社)]

    [5]

    Mei F X 2000 Appl. Mech. Rev. 53 283

    [6]

    Lou Z M 2006 Chin. Phys. 15 891

    [7]

    Zhang H B 2002 Chin. Phys. 11 1

    [8]

    Zhang R C 2000 Chin. Phys. 9 561

    [9]

    Lou Z M 2007 Chin. Phys. 16 1182

    [10]

    Wang S Y, Mei F X 2002 Chin. Phys. 11 5

    [11]

    Wang S Y, Mei F X 2001 Chin. Phys. 10 373

    [12]

    Mei F X, Zheng G H 2002 Acta Mech. Sin. 18 414

    [13]

    Mei F X 2002 Chin. Sci. Bull. 47 2019

    [14]

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

    [15]

    Xie J F, Gang T Q, Mei F X 2008 Chin. Phys. B 17 390

    [16]

    Sarlet W, Cantrijn F 1981 J. Phys. A: Math. Gen. 14 2227

    [17]

    Hojman S A1983 J. Phys. A: Math. Gen. 16 1383

    [18]

    Bloch A M, Krishnaprasad P S, Marsden J E, Murray R M 1996 Arch. Rational Mech. Anal. 136 21

    [19]

    Kara A, Mahomed F 2000 Int. J. Theor. Phys. 39 23

    [20]

    Beksert X, Park J H 2009 Eur. Phys. J. C 61 141

    [21]

    Jiang W A, Li Z J, Lou S K 2011 Chin. Phys. B 20 030202

    [22]

    Dong W S, Huang B X, Fang J H 2011 Chin. Phys. B 20 010204

计量
  • 文章访问数:  2994
  • PDF下载量:  666
  • 被引次数: 0
出版历程
  • 收稿日期:  2011-03-14
  • 修回日期:  2011-04-23
  • 刊出日期:  2012-01-05

力学系统的二阶梯度表示

  • 1. 绍兴文理学院物理系, 绍兴 312000;
  • 2. 北京理工大学力学系, 北京 100081
    基金项目: 

    国家自然科学基金重点项目

    (批准号: 10932002)资助的课题.

摘要: 研究力学系统运动微分方程的梯度表示以及二阶梯度表示. 将完整和非完整力学系统的微分方程在正则坐标下表出. 给出系统成为梯度系统以及二阶梯度系统的条件. 举例说明结果的应用.

English Abstract

参考文献 (22)

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