事件空间中Herglotz型非保守Lagrange系统的Noether定理  

Noether’s Theorem for Herglotz-Type Nonconservative Lagrange Systems in Event Space

作　　者：蔡锦祥 张毅[1] CAI Jinxiang;ZHANG Yi(College of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,Jiangsu,China)

机构地区：[1]苏州科技大学土木工程学院,江苏苏州215011

出　　处：《力学季刊》2022年第1期122-131,共10页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(11972241,11572212);江苏省自然科学基金(BK20191454)。

摘　　要：研究事件空间中Herglotz型非保守Lagrange系统的Noether定理.首先,将Herglotz广义变分原理推广到事件空间,并基于该原理导出事件空间中Herglotz型Lagrange方程;其次,引入无限小变换,研究Hamilton-Herglotz作用量的不变性,建立事件空间中Herglotz型Noether对称性的定义,并给出其判据方程;第三,提出并证明事件空间中Herglotz型Noether定理和Noether逆定理.最后,以Emden方程和黏性阻尼振子为例介绍Herglotz型Noether定理的应用.Noether’s theorem for Herglotz-type nonconservative Lagrange systems in event space are studied.Firstly,Herglotz’s generalized variational principle is extended to event space,and Herglotz-type Lagrange equations in event space are deduced from this principle.Secondly,the infinitesimal transformation is introduced to study the invariance of Hamilton-Herglotz action.The definition of Herglotz-type Noether symmetry in event space is set up,and the criterion equations are given.Thirdly,Noether’s theorem of Herglotz type in event space and its inverse are proposed and proved.Finally,Emden equation and viscous damped oscillator are taken as examples to demonstrate the application of Herglotz-type Noether’s theorem.

关 键 词：非保守Lagrange系统 Herglotz广义变分原理 NOETHER定理 事件空间 

分 类 号：O316[理学—一般力学与力学基础]