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.
作者
董欣畅
张毅
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)
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)。
