Recent Advances on Herglotz’s Generalized Variational Principle of Nonconservative Dynamics  

非保守动力学的Herglotz广义变分原理的研究进展

作　　者：ZHANG Yi 张毅(苏州科技大学土木工程学院,中国苏州215011)

机构地区：[1]College of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,P.R.China

出　　处：《Transactions of Nanjing University of Aeronautics and Astronautics》2020年第1期13-26,共14页南京航空航天大学学报（英文版）

基　　金：supported by the National Natural Science Foundations of China (Nos. 11972241,11572212,11272227);the Natural Science Foundation of Jiangsu Province(No. BK20191454).

摘　　要：This paper summarized the recent development on Herglotz’s generalized variational principle and its symmetries and conserved quantities for nonconservative dynamical systems.Taking Lagrangian mechanics,Hamiltonian mechanics and Birkhoffian mechanics as three research frames,we introduce Herglotz’s generalized variational principle,dynamical equations of Herglotz type,Noether symmetry and conserved quantities,and their generalization to time-delay dynamics,fractional dynamics and time-scale dynamics,and put forward some problems as suggestions for future research.综述非保守动力学系统的Herglotz广义变分原理及其对称性与守恒量研究的最新进展。以Lagrange力学、Hamilton力学和Birkhoff力学作为研究框架,介绍其Herglotz广义变分原理、Herglotz型动力学方程、Noether对称性与守恒量,以及对时滞动力学、分数阶动力学、时间尺度动力学的推广,并提出若干问题作为未来研究的建议。

关 键 词：nonconservative dynamics Herglotz’s generalized variational principle Lagrangian mechanics Hamil-tonian mechanics Birkhoffian mechanics 

分 类 号：O316[理学—一般力学与力学基础]