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变质量Chetaev型非完整系统Appell方程Mei对称性的共形不变性与守恒量

张芳 李伟 张耀宇 薛喜昌 贾利群

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变质量Chetaev型非完整系统Appell方程Mei对称性的共形不变性与守恒量

张芳, 李伟, 张耀宇, 薛喜昌, 贾利群

Conformal invariance and conserved quantity of Mei symmetry for Appell equations in nonholonomic systems of Chetaev’s type with variable mass

Zhang Fang, Li Wei, Zhang Yao-Yu, Xue Xi-Chang, Jia Li-Qun
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  • 研究了变质量Chetaev型非完整系统Appell方程Mei对称性的共形不变性和守恒量. 在群的无限小变换下,定义了变质量Chetaev型非完整系统Appell方程Mei对称性和共形不变性,给出了该系统Mei对称性的共形不变性确定方程,并推导出系统相应的守恒量表达式. 最后,给出了应用算例.
    Conformal invariance and conserved quantity of Mei symmetry for Appell equations of nonholonomic system of Chetaev's type with variable mass are studied. The conformal invariance and Mei symmetry for Appell equations of nonholonomic systems of Chetaev's type with variable mass are defined under the infinitesimal transformation of group, and the determining equations of conformal invariance of Mei symmetry for the system are given. Then, the expression of the corresponding conserved quantity of the system is derived. Finally, an example is given to illustrate the application of the results.
    • 基金项目: 国家自然科学基金(批准号:11142014)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11142014).
    [1]

    Noether A E 1918 Nachr. Akad. Wiss. Göttingen Math-Phys. 2 235

    [2]

    Mei F X, Wu H B 2010 Chin. Phys. B 19 050301

    [3]

    Mei F X 2003 Acta Phys. Sin. 52 1048 (in Chinese) [梅凤翔 2003 物理学报 52 1048]

    [4]

    Luo S K, Li L 2013 Nonlinear Dyn. 73 639

    [5]

    Luo S K, Li L 2013 Nonlinear Dyn. 73 339

    [6]

    Luo S K, Li Z J, Peng W, Li L 2013 Acta Mech. 224 71

    [7]

    Luo S K, Li Z J, Li L 2012 Acta Mech. 223 2621

    [8]

    Jia L Q, Wang X X, Zhang M L, Han Y L 2012 Nonlinear Dyn. 69 1807

    [9]

    Han Y L, Wang X X, Zhang M L, Jia L Q 2014 J. Mech. 30 21

    [10]

    Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 71 401

    [11]

    Wang X X, Han Y L, Zhang M L, Jia L Q 2013 Chin. Phys. B 22 020201

    [12]

    Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Acta Phys. Sin. 62 110201 (in Chinese) [韩月林, 王肖肖, 张美玲, 贾利群 2013 物理学报 62 110201]

    [13]

    Galiullin A S, Gafarov G G, Malaishka R P, Khwan A M 1997 Analytical Dynamics of Helmholtz, Birhoff and Nambu Systems (Moscow: UFN) p183 (in Russian)

    [14]

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

    [15]

    Cai J L, Shi S S, Fang H J, Xu J 2012 Meccanica 47 63

    [16]

    Zhang Y 2009 Chin. Phys. B 18 4636

    [17]

    Huang W L, Cai J L 2012 Acta Mech. 223 433

    [18]

    Cai J L 2012 Nonlinear Dyn. 69 487

    [19]

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

    [20]

    Zhang Y 2010 Commun. Theor. Phys. 53 166

    [21]

    Wu H B, Mei F X 2012 Chin. Phys. B 21 064501

    [22]

    Chen X W, Zhao Y H, Liu C 2009 Acta Phys. Sin. 58 5150 (in Chinese) [陈向炜, 赵永红, 刘畅 2009 物理学报 58 5150]

    [23]

    Cai J L, Shi S S 2012 Acta Phys. Sin. 61 030201 (in Chinese) [蔡建乐, 史生水 2012 物理学报 61 030201]

    [24]

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

    [25]

    Han Y L, Sun X T, Zhang Y Y, Jia L Q 2013 Acta Phys. Sin. 62 160201 (in Chinese) [韩月林, 孙现亭, 张耀宇, 贾利群 2013 物理学报 62 160201]

    [26]

    Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) p168 (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) 第168页]

    [27]

    Zheng S W, Wang J B, Chen X W, Li Y M, Xie J F 2012 Acta Phys. Sin. 61 111101 (in Chinese) [郑世旺, 王建波, 陈向炜, 李彦敏, 解加芳 2012 物理学报 61 111101]

    [28]

    Xu C, Li Y C 2013 Acta Phys. Sin. 62 171101 (in Chinese) [徐超, 李元成 2013 物理学报 62 171101]

    [29]

    Jia L Q, Sun X T, Zhang M L, Zhang Y Y, Han Y L 2014 Acta Phys. Sin. 63 010201 (in Chinese) [贾利群, 孙现亭, 张美玲, 张耀宇, 韩月林 2014 物理学报 63 010201]

    [30]

    Zhang B, Fang J H, Zhang K J 2012 Acta Phys. Sin. 61 021101 (in Chinese) [张斌, 方建会, 张克军 2012 物理学报 61 021101]

  • [1]

    Noether A E 1918 Nachr. Akad. Wiss. Göttingen Math-Phys. 2 235

    [2]

    Mei F X, Wu H B 2010 Chin. Phys. B 19 050301

    [3]

    Mei F X 2003 Acta Phys. Sin. 52 1048 (in Chinese) [梅凤翔 2003 物理学报 52 1048]

    [4]

    Luo S K, Li L 2013 Nonlinear Dyn. 73 639

    [5]

    Luo S K, Li L 2013 Nonlinear Dyn. 73 339

    [6]

    Luo S K, Li Z J, Peng W, Li L 2013 Acta Mech. 224 71

    [7]

    Luo S K, Li Z J, Li L 2012 Acta Mech. 223 2621

    [8]

    Jia L Q, Wang X X, Zhang M L, Han Y L 2012 Nonlinear Dyn. 69 1807

    [9]

    Han Y L, Wang X X, Zhang M L, Jia L Q 2014 J. Mech. 30 21

    [10]

    Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 71 401

    [11]

    Wang X X, Han Y L, Zhang M L, Jia L Q 2013 Chin. Phys. B 22 020201

    [12]

    Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Acta Phys. Sin. 62 110201 (in Chinese) [韩月林, 王肖肖, 张美玲, 贾利群 2013 物理学报 62 110201]

    [13]

    Galiullin A S, Gafarov G G, Malaishka R P, Khwan A M 1997 Analytical Dynamics of Helmholtz, Birhoff and Nambu Systems (Moscow: UFN) p183 (in Russian)

    [14]

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

    [15]

    Cai J L, Shi S S, Fang H J, Xu J 2012 Meccanica 47 63

    [16]

    Zhang Y 2009 Chin. Phys. B 18 4636

    [17]

    Huang W L, Cai J L 2012 Acta Mech. 223 433

    [18]

    Cai J L 2012 Nonlinear Dyn. 69 487

    [19]

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

    [20]

    Zhang Y 2010 Commun. Theor. Phys. 53 166

    [21]

    Wu H B, Mei F X 2012 Chin. Phys. B 21 064501

    [22]

    Chen X W, Zhao Y H, Liu C 2009 Acta Phys. Sin. 58 5150 (in Chinese) [陈向炜, 赵永红, 刘畅 2009 物理学报 58 5150]

    [23]

    Cai J L, Shi S S 2012 Acta Phys. Sin. 61 030201 (in Chinese) [蔡建乐, 史生水 2012 物理学报 61 030201]

    [24]

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

    [25]

    Han Y L, Sun X T, Zhang Y Y, Jia L Q 2013 Acta Phys. Sin. 62 160201 (in Chinese) [韩月林, 孙现亭, 张耀宇, 贾利群 2013 物理学报 62 160201]

    [26]

    Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) p168 (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) 第168页]

    [27]

    Zheng S W, Wang J B, Chen X W, Li Y M, Xie J F 2012 Acta Phys. Sin. 61 111101 (in Chinese) [郑世旺, 王建波, 陈向炜, 李彦敏, 解加芳 2012 物理学报 61 111101]

    [28]

    Xu C, Li Y C 2013 Acta Phys. Sin. 62 171101 (in Chinese) [徐超, 李元成 2013 物理学报 62 171101]

    [29]

    Jia L Q, Sun X T, Zhang M L, Zhang Y Y, Han Y L 2014 Acta Phys. Sin. 63 010201 (in Chinese) [贾利群, 孙现亭, 张美玲, 张耀宇, 韩月林 2014 物理学报 63 010201]

    [30]

    Zhang B, Fang J H, Zhang K J 2012 Acta Phys. Sin. 61 021101 (in Chinese) [张斌, 方建会, 张克军 2012 物理学报 61 021101]

计量
  • 文章访问数:  1699
  • PDF下载量:  336
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-04-08
  • 修回日期:  2014-04-24
  • 刊出日期:  2014-08-05

变质量Chetaev型非完整系统Appell方程Mei对称性的共形不变性与守恒量

  • 1. 平顶山学院电气信息工程学院, 平顶山 467002;
  • 2. 河南城建学院数理学院, 平顶山 467002;
  • 3. 江南大学理学院, 无锡 214122
    基金项目: 

    国家自然科学基金(批准号:11142014)资助的课题.

摘要: 研究了变质量Chetaev型非完整系统Appell方程Mei对称性的共形不变性和守恒量. 在群的无限小变换下,定义了变质量Chetaev型非完整系统Appell方程Mei对称性和共形不变性,给出了该系统Mei对称性的共形不变性确定方程,并推导出系统相应的守恒量表达式. 最后,给出了应用算例.

English Abstract

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