Noether Theorem of Herglotz-Type for Nonconservative Hamilton Systems in Event Space  

作　　者：ZHANG Yi CAI Jinxiang 

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

出　　处：《Wuhan University Journal of Natural Sciences》2021年第5期376-382,共7页武汉大学学报（自然科学英文版）

基　　金：Supported by the National Natural Science Foundation of China (11972241, 11572212);the Natural Science Foundation of Jiangsu Province (BK20191454)。

摘　　要：Focusing on the exploration of symmetry and conservation laws in event space, this paper studies Noether theorems of Herglotz-type for nonconservative Hamilton system. Herglotz’s generalized variational principle is first extended to event space,and on this basis, Hamilton equations of Herglotz-type in event space are derived. The invariance of Hamilton-Herglotz action is then studied by introducing infinitesimal transformation, and the definition of Herglotz-type Noether symmetry in event space is given, and its criterion is derived. Noether theorem of Herglotz-type and its inverse for event space nonconservative Hamilton system are proved. The application of Herglotz-type Noether theorem we obtained is introduced by taking Emden-Fowler equation and linearly damped oscillator as examples.

关 键 词：Herglotz’s generalized variational principle Noether theorem nonconservative Hamilton system event space 

分 类 号：O316[理学—一般力学与力学基础]