二阶非完整系统Vacco动力学的Herglotz型Noether定理  

Herglotz-Type Noether Theorem for Vacco Dynamics of Second-Order Nonholonomic Systems

作　　者：黄丽琴 张毅[2] Huang Liqin;Zhang Yi(School of Mathematical Sciences,Suzhou University of Science and Technology,Suzhou 215009,China;School 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9期16-23,共8页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(12272248,11972241)。

摘　　要：研究二阶非完整系统Vacco动力学的Herglotz型Noether定理.首先,基于Herglotz广义变分原理,建立了二阶非完整系统Vacco动力学的Herglotz型运动微分方程.其次,根据Hamilton-Herglotz作用量的非等时变分公式,给出了二阶非完整系统Vacco动力学的Herglotz型Noether对称性和准对称性的概念及其判据方程,并推导了系统的Herglotz型Noether定理及其逆定理.最后,举例说明了该结果的应用.The Herglotz-type Noether theorems for the Vacco dynamics of second-order nonholonomic systems are studied.Firstly,based on the Herglotz generalized variational principle,the Herglotz-type differential equations of motion for Vacco dynamics of second-order nonholonomic systems are established.Secondly,according to the non-isochronous variation formulas of Hamilton-Herglotz action,the concepts of Herglotz-type Noether symmetry and quasi-symmetry and their criterion equations for Vacco dynamics of second-order nonholonomic systems are given,and the Herglotz-type Noether theorems and their inverse theorems are further derived.Finally,an example is given to illustrate the application of the results.

关 键 词：二阶非完整系统 VACCO动力学 Herglotz变分原理 NOETHER定理 

分 类 号：O316[理学—一般力学与力学基础]