非保守非完整系统的Herglotz型Noether定理
Herglotz-Type Noether Theorem for Nonconservative Nonholonomic System
董欣畅 1张毅2
作者信息
- 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
- 折叠
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Her-glotz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.
Abstract
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Key words
nonholonomic system/Herglotz variational principle/Noether's theorem引用本文复制引用
基金项目
国家自然科学基金资助项目(12272248)
国家自然科学基金资助项目(11972241)
江苏省研究生科研创新计划资助项目(KYCX22_3251)
出版年
2024
NETL
NSTL
万方数据