相空间中Herglotz型微分变分原理与一类新型绝热不变量  

Differential variational principle of Herglotz type and a new type of adiabatic invariants in phase space

作　　者：徐鑫鑫 张毅[2] XU Xinxin;ZHANG Yi(College of Mathematics and Physics,Suzhou University of Science and Technology,Suzhou 215009,China;College of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,China)

机构地区：[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

出　　处：《中山大学学报（自然科学版）》2020年第1期35-42,共8页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金(11572212,19972241);江苏省自然科学基金(BK20191454);江苏省普通高校研究生科研创新计划项目(KYCX18_2548)

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。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.

关 键 词：非保守系统 Herglotz型微分变分原理 绝热不变量 相空间 

分 类 号：O316[理学—一般力学与力学基础]