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Chetaev型非完整系统Mei对称性的共形不变性与守恒量

蔡建乐 史生水

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Chetaev型非完整系统Mei对称性的共形不变性与守恒量

蔡建乐, 史生水

Conformal invariance and conserved quantity of Mei symmetry for the nonholonomic system of Chetaev's type

Cai Jian-Le, Shi Sheng-Shui
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  • 研究Chetaev型非完整系统Mei对称性的共形不变性与守恒量. 引入无限小单参数变换群及其生成元向量,给出与Chetaev型非完整系统相应的完整系统的Mei对称性共形 不变性定义和确定方程,讨论系统共形不变性与Mei对称性的关系.利用限制方程和附加限制方程得到非完整 系统弱Mei对称性和强Mei对称性的共形不变性.借助规范函数满足的结构方程导出系统相应的守恒量, 并举例说明结果的应用.
    For a nonholonomic system of Chetaev's type, the conformal invariance and the conserved quantity are studied. By the infinitesimal one-parameter transformation group and the infinitesimal generator vector, the definition of conformal invariance of Mei symmetry and the determining equation for the holonomic system which corresponds to a nonholonomic system are provided, and the relationship between the system conformal invariance and Mei symmetry is discussed. Using the restriction equations and the additional restriction equations, the conformal invariances of weak and strong Mei symmetrys for the system are given. With the aid of a structure equation that gauge function satisfies, the system corresponding conserved quantity is derived. Finally, an example is given to illustrate the application of the result.
    • 基金项目: 国家自然科学基金(批准号:10772025)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 10772025).
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    [2]

    Djukić D S, Vujanović B D 1975 Acta Mechanica 23 17

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    [4]

    Zhao Y Y, Mei F X 1999 Symmetries and Invariants of MechanicalSystems (Beijing: Science Press)(in Chinese) [赵跃宇, 梅凤翔 1999 力学系统的对称性与不变量(北京:科学出版社)]

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

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    Ge W K 2002 Acta Phys. Sin. 51 1156 (in Chinese) [葛伟宽 2002 物理学报 51 1156]

    [7]

    Fang J H 2003 Commun. Theor. Phys. 40 269

    [8]

    Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of TechnologyPress) (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)]

    [9]

    Jiang W A, Li L, Li Z J, Luo S K 2012 Nonlinear Dyn. 67 1075

    [10]

    Li Z J, Jiang W A, Luo S K 2012 Nonlinear Dyn. 67 445

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    Luo S K 2007 Chin. Phys. Lett. 24 2463

    [12]

    Jia L Q, Zhang Y Y, Zheng S W 2007 Acta Phys. Sin. 56 649 (in Chinese) [贾利群,张耀宇,郑世旺 2007物理学报 56 649]

    [13]

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

    [14]

    Luo S K , Zhang Y F 2008 Advances in the Study of Dynamics ofConstrained Systems (Beijing: Science Press) (in Chinese) [罗绍凯,张永发 2008 约束系统动力学研究进展(北京:科学出版社)]

    [15]

    Galiullin A S, Gafarov G G, Malaishka R P, Khwan A M 1997Analytical Dynamics of Helmholtz, Birkhoff and Nambu Systems(Moscow: UFN) (in Russian)

    [16]

    Cai J L 2008 Chin. Phys. Lett. 25 1523

    [17]

    Mei F X, Xie J F, Gang T Q 2008 Acta Mech. Sin. 24 583

    [18]

    He G, Mei F X 2008 Chin. Phys. B 17 2764

    [19]

    Cai J L, Mei F X 2008 Acta Phys. Sin. 57 5369 (in Chinese) [蔡建乐,梅凤翔 2008 物理学报 57 5369]

    [20]

    Cai J L, Luo S K, Mei F X 2008 Chin. Phys. B 17 3170

    [21]

    Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 物理学报 58 22]

    [22]

    Cai J L 2009 Acta Phys. Pol. A 115 854

    [23]

    Xia L L, Cai J L, Li Y C 2009 Chin. Phys. B 18 3158

    [24]

    Luo Y P 2009 Int. J. Theor. Phys. 48 2665

    [25]

    Li Y C, Xia L L, Wang X M 2009 Chin. Phys. B 18 4643

    [26]

    Zhang M J, Fang J H, Lin P, Lu K, Pang T 2009 Commun. Theor.Phys. 52 561

    [27]

    Chen X W, Li Y M, Zhao Y H 2009 Chin. Phys. B 18 3139

    [28]

    Zhang Y 2009 Chin. Phys. B 18 4636

    [29]

    Cai J L 2010 Acta Phys. Pol. A 117 445

    [30]

    Xia L L, Cai J L 2010 Chin. Phys. B 19 040302

    [31]

    Zhang Y 2010 Commun. Theor. Phys. 53 166

    [32]

    Luo Y P, Fu J L 2010 Chin. Phys. B 19 090303

    [33]

    Luo Y P, Fu J L 2010 Chin. Phys. B 19 090304

    [34]

    Luo Y P, Fu J L 2011 Chin. Phys. B 20 021102

    [35]

    Li Y, Fang J H, Zhang K J 2011 Chin. Phys. B 20 030201

    [36]

    Cai J L 2010 Int. J. Theor. Phys. 49 201

  • [1]

    Noether A E 1918 Nachr. Akad. Math. 2 235

    [2]

    Djukić D S, Vujanović B D 1975 Acta Mechanica 23 17

    [3]

    Mei F X 1999 Applications of Lie Groups and Lie Algebras to ConstrainedMechanical 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)]

    [4]

    Zhao Y Y, Mei F X 1999 Symmetries and Invariants of MechanicalSystems (Beijing: Science Press)(in Chinese) [赵跃宇, 梅凤翔 1999 力学系统的对称性与不变量(北京:科学出版社)]

    [5]

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

    [6]

    Ge W K 2002 Acta Phys. Sin. 51 1156 (in Chinese) [葛伟宽 2002 物理学报 51 1156]

    [7]

    Fang J H 2003 Commun. Theor. Phys. 40 269

    [8]

    Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of TechnologyPress) (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)]

    [9]

    Jiang W A, Li L, Li Z J, Luo S K 2012 Nonlinear Dyn. 67 1075

    [10]

    Li Z J, Jiang W A, Luo S K 2012 Nonlinear Dyn. 67 445

    [11]

    Luo S K 2007 Chin. Phys. Lett. 24 2463

    [12]

    Jia L Q, Zhang Y Y, Zheng S W 2007 Acta Phys. Sin. 56 649 (in Chinese) [贾利群,张耀宇,郑世旺 2007物理学报 56 649]

    [13]

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

    [14]

    Luo S K , Zhang Y F 2008 Advances in the Study of Dynamics ofConstrained Systems (Beijing: Science Press) (in Chinese) [罗绍凯,张永发 2008 约束系统动力学研究进展(北京:科学出版社)]

    [15]

    Galiullin A S, Gafarov G G, Malaishka R P, Khwan A M 1997Analytical Dynamics of Helmholtz, Birkhoff and Nambu Systems(Moscow: UFN) (in Russian)

    [16]

    Cai J L 2008 Chin. Phys. Lett. 25 1523

    [17]

    Mei F X, Xie J F, Gang T Q 2008 Acta Mech. Sin. 24 583

    [18]

    He G, Mei F X 2008 Chin. Phys. B 17 2764

    [19]

    Cai J L, Mei F X 2008 Acta Phys. Sin. 57 5369 (in Chinese) [蔡建乐,梅凤翔 2008 物理学报 57 5369]

    [20]

    Cai J L, Luo S K, Mei F X 2008 Chin. Phys. B 17 3170

    [21]

    Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 物理学报 58 22]

    [22]

    Cai J L 2009 Acta Phys. Pol. A 115 854

    [23]

    Xia L L, Cai J L, Li Y C 2009 Chin. Phys. B 18 3158

    [24]

    Luo Y P 2009 Int. J. Theor. Phys. 48 2665

    [25]

    Li Y C, Xia L L, Wang X M 2009 Chin. Phys. B 18 4643

    [26]

    Zhang M J, Fang J H, Lin P, Lu K, Pang T 2009 Commun. Theor.Phys. 52 561

    [27]

    Chen X W, Li Y M, Zhao Y H 2009 Chin. Phys. B 18 3139

    [28]

    Zhang Y 2009 Chin. Phys. B 18 4636

    [29]

    Cai J L 2010 Acta Phys. Pol. A 117 445

    [30]

    Xia L L, Cai J L 2010 Chin. Phys. B 19 040302

    [31]

    Zhang Y 2010 Commun. Theor. Phys. 53 166

    [32]

    Luo Y P, Fu J L 2010 Chin. Phys. B 19 090303

    [33]

    Luo Y P, Fu J L 2010 Chin. Phys. B 19 090304

    [34]

    Luo Y P, Fu J L 2011 Chin. Phys. B 20 021102

    [35]

    Li Y, Fang J H, Zhang K J 2011 Chin. Phys. B 20 030201

    [36]

    Cai J L 2010 Int. J. Theor. Phys. 49 201

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出版历程
  • 收稿日期:  2011-03-27
  • 修回日期:  2011-06-15
  • 刊出日期:  2012-03-15

Chetaev型非完整系统Mei对称性的共形不变性与守恒量

  • 1. 杭州师范大学理学院, 杭州 310018
    基金项目: 国家自然科学基金(批准号:10772025)资助的课题.

摘要: 研究Chetaev型非完整系统Mei对称性的共形不变性与守恒量. 引入无限小单参数变换群及其生成元向量,给出与Chetaev型非完整系统相应的完整系统的Mei对称性共形 不变性定义和确定方程,讨论系统共形不变性与Mei对称性的关系.利用限制方程和附加限制方程得到非完整 系统弱Mei对称性和强Mei对称性的共形不变性.借助规范函数满足的结构方程导出系统相应的守恒量, 并举例说明结果的应用.

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