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高阶非完整约束系统嵌入变分恒等式的积分变分原理

宋端 刘畅 郭永新

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高阶非完整约束系统嵌入变分恒等式的积分变分原理

宋端, 刘畅, 郭永新

The integral variational principles for embedded variation identity of high-order nonholonomic constrained systems

Song Duan, Liu Chang, Guo Yong-Xin
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  • 本文从高阶非完整系统嵌入变分恒等式的积分变分原理出发, 根据三种不等价条件变分的选取, 得到了高阶非完整系统的三类不等价动力学模型, 即高阶非完整约束系统的vakonomic方程、Lagrange-d'Alembert 方程和一种新的动力学方程. 当高阶非完整约束方程退化为一阶非完整约束时, 利用此理论可以得到一般非完整系统的vakonomic模型、Chetaev模型和一种新的动力学模型. 最后借助于应用实例验证了结论的正确性.
    In this article, from the integral variational principles for embedded variation identity of high-order nonholonomic constrained systems, three kinds of dynamics for high-order nonholonomic constrained systems are obtained, including the vakonomic dynamical model, Lagrange-d'Alembert model and a new one if utilizing respectively three kinds of conditional variation to them. And the integral variational principles for embedded variation identity of high-order nonholonomic constrained systems is also fitted for the general nonholonomic systems when the constrained equation is reduced to a first-order one. Then, the vakonomic dynamic, Chetaev dynamics and a new model of general nonholonomic systems can also be obtained. Finally, two illustrated examples are used to verify the validity of the theory.
    • 基金项目: 国家自然科学基金(批准号:11202090,11172120,10932002)和辽宁省重点实验室建设项目(批准号:2008403009)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11202090, 11172120, 10932002) and the Program of Constructing Liaoning Provincial Key Laboratory, China (Grant No. 2008403009).
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    Shen H C 2005 Acta Phys. Sin. 54 6 (in Chinese) [沈惠川 2005 物理学报 54 6]

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    Guo Y X, Zhao Z, Liu S X, Liu C 2008 Acta Phys. Sin. 57 3 (in Chinese) [郭永新, 赵喆, 刘世兴, 刘畅 2008 物理学报 57 3]

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    Zhao Z, Guo Y X, Liu C, Liu S X 2008 Acta Phys. Sin. 57 4 (in Chinese) [赵喆, 郭永新, 刘畅, 刘世兴 2008 物理学报 57 4]

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    Guo Z H, Gao P Y 1992 Chinese Journal of Theoretical and Applied Mechanics 24 2 (in Chinese) [郭仲衡, 高普云 1992 力学学报 24 2]

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    Guo Y X, Zhao Z, Liu S X, Zhu N, Han X J 2006 Acta Phys. Sin. 55 8 (in Chinese) [郭永新, 赵喆, 刘世兴, 朱娜, 韩晓静 2006 物理学报 55 8]

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    Guo Y X, Liu S X, Liu C, Chang P 2009 Phys. Lett. A 373

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    Zheng X Y, Wu Y Q 2009 Int. J. Auto. Comp. 6 3

    [13]

    Gao F Z, Yuan F S, Gao C C 2009 Fuzzy Systems and Mathematics 23 3 (in Chinese) [高芳征, 袁付顺, 高存臣 2009 模糊系统与数学 23 3]

    [14]

    Zhang X W 2006 Journal of Longdong College 16 1 (in Chinese) [张相武 2006 陇东学院学报 16 1]

    [15]

    Mu X W, Yu J M, Cheng G F 2006 Applied Mathematics and Mechanics 27 4 (in Chinese) [慕小武, 虞继敏, 程桂芳 2006 应用数学和力学 27 4]

    [16]

    Gao F Z, Shang Y L, Yuan F S 2012 Journal of System Sciences and Mathematical Sciences 32 2 (in Chinese) [高芳征, 尚艳玲, 袁付顺 2012 系统科学与数学 32 2]

    [17]

    Mei F X, Shi R C, Zhang Y F, Wu H B 1996 Dynamics of Birkhoffian Systems (Beijing: Beijing Institute Technology Press) (in Chinese) [梅凤翔, 史荣昌, 张永发, 吴惠彬 1996 Birkhoff 系统动力学 (北京: 北京理工大学出版)]

    [18]

    Mei F X 1991 Applied Mathematics and Mechanics 12 8 (in Chinese) [梅凤翔 1991 应用数学和力学 12 8]

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    Chen L Q 1992 Journal of Anshan Institute I. & S. Technology 15 1 (in Chinese) [陈立群 1992 鞍山钢铁学院学报 15 1]

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  • [1]

    Guo Y X, Luo S K, Mei F X 2004 Advance in Mechanics 34 3 (in Chinese) [郭永新, 罗绍凯, 梅凤翔 2004 力学进展 34 3]

    [2]

    Neimark Ju I, Fufaev N A 1972 Dynamics of Nonholonomic Systems Providence: American Mathematical Society

    [3]

    Mei F X, Liu D, Luo Y 1991 Advanced Analytical Mechanics (Beijing: Beijing Institute Technology Press) (in Chinese) [梅凤翔, 刘瑞, 罗勇 1991 高等分析力学 (北京: 北京理工大学出版社)]

    [4]

    Shen H C 2005 Acta Phys. Sin. 54 6 (in Chinese) [沈惠川 2005 物理学报 54 6]

    [5]

    Guo Y X, Zhao Z, Liu S X, Liu C 2008 Acta Phys. Sin. 57 3 (in Chinese) [郭永新, 赵喆, 刘世兴, 刘畅 2008 物理学报 57 3]

    [6]

    Zhao Z, Guo Y X, Liu C, Liu S X 2008 Acta Phys. Sin. 57 4 (in Chinese) [赵喆, 郭永新, 刘畅, 刘世兴 2008 物理学报 57 4]

    [7]

    Guo Z H, Gao P Y 1990 Chinese Journal of Theoretical and Applied Mechanics 22 2 (in Chinese) [郭仲衡, 高普云 1990 力学学报 22 2]

    [8]

    Chen B 1991 Chinese Journal of Theoretical and Applied Mechanics 23 3 (in Chinese) [陈滨 1991 力学学报 23 3]

    [9]

    Guo Z H, Gao P Y 1992 Chinese Journal of Theoretical and Applied Mechanics 24 2 (in Chinese) [郭仲衡, 高普云 1992 力学学报 24 2]

    [10]

    Guo Y X, Zhao Z, Liu S X, Zhu N, Han X J 2006 Acta Phys. Sin. 55 8 (in Chinese) [郭永新, 赵喆, 刘世兴, 朱娜, 韩晓静 2006 物理学报 55 8]

    [11]

    Guo Y X, Liu S X, Liu C, Chang P 2009 Phys. Lett. A 373

    [12]

    Zheng X Y, Wu Y Q 2009 Int. J. Auto. Comp. 6 3

    [13]

    Gao F Z, Yuan F S, Gao C C 2009 Fuzzy Systems and Mathematics 23 3 (in Chinese) [高芳征, 袁付顺, 高存臣 2009 模糊系统与数学 23 3]

    [14]

    Zhang X W 2006 Journal of Longdong College 16 1 (in Chinese) [张相武 2006 陇东学院学报 16 1]

    [15]

    Mu X W, Yu J M, Cheng G F 2006 Applied Mathematics and Mechanics 27 4 (in Chinese) [慕小武, 虞继敏, 程桂芳 2006 应用数学和力学 27 4]

    [16]

    Gao F Z, Shang Y L, Yuan F S 2012 Journal of System Sciences and Mathematical Sciences 32 2 (in Chinese) [高芳征, 尚艳玲, 袁付顺 2012 系统科学与数学 32 2]

    [17]

    Mei F X, Shi R C, Zhang Y F, Wu H B 1996 Dynamics of Birkhoffian Systems (Beijing: Beijing Institute Technology Press) (in Chinese) [梅凤翔, 史荣昌, 张永发, 吴惠彬 1996 Birkhoff 系统动力学 (北京: 北京理工大学出版)]

    [18]

    Mei F X 1991 Applied Mathematics and Mechanics 12 8 (in Chinese) [梅凤翔 1991 应用数学和力学 12 8]

    [19]

    Chen L Q 1992 Journal of Anshan Institute I. & S. Technology 15 1 (in Chinese) [陈立群 1992 鞍山钢铁学院学报 15 1]

    [20]

    Li Y, Fang J H, Zhang K J 2010 Journal of Dynamics and Control 8 4 (in Chinese) [李燕, 方建会, 张克军 2010 动力学与控制学报 8 4]

计量
  • 文章访问数:  4675
  • PDF下载量:  456
  • 被引次数: 0
出版历程
  • 收稿日期:  2012-11-30
  • 修回日期:  2012-12-30
  • 刊出日期:  2013-05-05

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