非保守非完整系统的Herglotz型Noether定理  

Herglotz-Type Noether Theorem for Nonconservative Nonholonomic System

作　　者：董欣畅 张毅[2] Dong Xinchang;Zhang Yi(School of Mathematical Sciences,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]苏州科技大学数学科学学院,苏州215009 [2]苏州科技大学土木工程学院,苏州215011

出　　处：《动力学与控制学报》2024年第5期1-7,共7页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(12272248,11972241);江苏省研究生科研创新计划资助项目(KYCX22_3251)。

摘　　要：研究非保守非完整系统的Herglotz型Noether定理及其逆定理.首先,将Herglotz变分原理推广到非保守非完整系统,并基于该原理推导出系统的带乘子型运动微分方程.其次,引入无限小变换,研究Herglotz作用量的不变性,提出并证明非保守非完整系统的Noether定理.再次,研究了对称性逆问题,给出了Noether逆定理.最后,以受非保守力的Appell-Hamel问题为例,介绍Herglotz型Noether定理的应用.The Herglotz-type Noether theorem and its inverse theorem for non-conservative nonholonom-ic systems are studied.Firstly,the Herglotz variational principle is extended to non-conservative non-holonomic systems,and the differential equation of motion with multipliers is derived based on this prin-ciple.Secondly,the infinitesimal transformation is introduced to study the invariance of Lagrange-Her-glotz action,and the Noether theorem for non-conservative nonholonomic systems is proposed and proved.Thirdly,the inverse problem of symmetry is studied and Noether's inverse theorem is given.Finally,taking Appell-Hamel problem subject to non-conservative forces as an example,we introduce the application of Herglotz type Noether theorem.

关 键 词：非完整系统 Herglotz变分原理 NOETHER定理 

分 类 号：O316[理学—一般力学与力学基础]