中山大学学报自然科学版 ›› 2016, Vol. 55 ›› Issue (6): 79-85.

• 研究论文 • 上一篇    下一篇

基于Caputo导数下的含时滞的Hamilton系统的分数阶Noether理论

丁金凤1,金世欣2,张毅3   

  1. 1.苏州科技大学数理学院,江苏 苏州 215009;
    2.南京理工大学理学院,江苏 南京 210094;
    3.苏州科技大学土木工程学院,江苏 苏州 215009
  • 收稿日期:2016-05-12 出版日期:2016-11-25 发布日期:2016-11-25
  • 通讯作者: 丁金凤(1983年生),女;研究方向:力学中的数学方法;Email:vividding@126.com

Fractional Noether theorems for Hamilton system with time delay based on Caputo dervitaves

DING Jinfeng1, JIN Shixin2, ZHANG Yi3   

  1. 1. College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China;
    2. College of Physics, Nanjing University of Science and Technology, Nanjing 210018, China;
    3. College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215009, China
  • Received:2016-05-12 Online:2016-11-25 Published:2016-11-25

摘要:

提出并讨论了Caputo导数定义下的含时滞的Hamilton系统的分数阶Noether对称性与守恒量。 根据含时滞的Hamilton系统的分数阶Hamilton原理,建立了相应的含时滞的分数阶Hamilton正则方程;依据分数阶Hamilton作用量在无限小变换下的不变性,得到了含时滞的Hamilton系统的分数阶Noether对称性;最后,建立了系统的含时滞的分数阶Noether理论,并举例说明结果的应用。

关键词: 时滞, Hamilton系统, Caputo导数, Noether对称性, 守恒量

Abstract:

The fractional Noether symmetries and fractional conserved quantities for Hamilton system with time delay based on Caputo derivatives are discussed. The fractional Hamilton canonical equations of the corresconding system with time delay are established base upon the fractional Hamilton principle of the Hamilton systems with time delay. Then, the fractional Noether symmetries of the Hamilton system with time delay are obtained, which based on the invariance of the fractional Hamilton action with time delay under the infinitesimal transformations of group. Finally, fractional Noether theorems with time delay of the Hamilton system are established. At the end, one example is given to illustrate the application of the results.

Key words: time delay, Hamilton system, Caputo derivatives, Noether symmetry, conserved quantity

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