中山大学学报(自然科学版) ›› 2020, Vol. 59 ›› Issue (1): 35-42.doi: 10.13471/j.cnki.acta.snus.2020.01.005

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相空间中Herglotz型微分变分原理与一类新型绝热不变量

XU Xinxin1,ZHANG Yi2   

  1. 1. 苏州科技大学数理学院,江苏 苏州 215009;
    2. 苏州科技大学土木工程学院,江苏 苏州 215011
  • 收稿日期:2019-03-08 出版日期:2020-01-25 发布日期:2020-02-28
  • 通讯作者: 张毅(1964年生),男;研究方向:力学中的数学方法;E-mail: zhy@mail.usts.edu.cn

Differential variational principle of Herglotz type and a new type of adiabatic invariants in phase space#br#
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徐鑫鑫1,张毅2   

  1. 1.College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China;
    2.College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China
  • Received:2019-03-08 Online:2020-01-25 Published:2020-02-28

摘要:

基于Herglotz型微分变分原理,研究了相空间中非保守系统的绝热不变量问题。首先,列写出基于Herglotz广义变分原理的Hamilton正则方程;其次,基于Hamilton-Herglotz作用量在群的无穷小变换下的不变性,给出了相空间中新型精确不变量,并进一步研究在小扰动作用下的摄动,得到了系统的一类新型绝热不变量;再次,给出了逆定理;最后,举例说明结果的应用。


关键词: 非保守系统, Herglotz型微分变分原理, 绝热不变量, 相空间

Abstract:

According to differential variational principle of Herglotz type, this paper studies the adiabatic invariants for nonconservative system in phase space. Firstly, the Hamilton canonical equations based upon the generalized variational principle of Herglotz are given. Secondly, by using the invariance of the Hamilton-Herglotz action under the infinitesimal transformations, the new type of exact invariants in phase space are established, and the perturbation of the system with the action of small disturbance is investigated, and a new type of adiabatic invariants of the system are obtained. Thirdly, the inverse theorem is given. In the end of the paper, an example is given to illustrate the application of the results.


Key words: non-conservative system, differential variational principle of Herglotz type, adiabatic invariants, phase space

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