基于分数阶模型的非完整系统的Mei对称性及其守恒量  

Mei Symmetry and Its Conserved Quantities of Nonholonomic Systems Based on Fractional Models

作　　者：王璐 张毅[2] WANG Lu;ZHANG Yi(School of Mathematical Sciences,Suzhou University of Science and Technology,Suzhou 215009,Jiangsu,China;College of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,Jiangsu,China)

机构地区：[1]苏州科技大学数学科学学院,江苏苏州215009 [2]苏州科技大学土木工程学院,江苏苏州215011

出　　处：《力学季刊》2023年第3期633-642,共10页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(12272248,11972241);江苏省研究生科研创新计划项目(KYCX21_3002)。

摘　　要：为了进一步揭示非完整系统的对称性和守恒量之间的内在关系,提出并研究基于分数阶模型的非完整系统的Mei对称性及其守恒量.首先,根据分数阶d’Alembert-Lagrange原理建立基于分数阶模型的非完整系统的动力学方程.其次,根据动力学方程中的动力学函数经无限小变换后仍满足原方程的不变性,建立分数阶模型下非完整系统的Mei对称性定理,给出Mei守恒量.再次,讨论了几个特例:分数阶Hamilton系统、经典非完整系统和受非完整约束的分数阶Lagrange系统的Mei对称性定理.文末举例说明结果的应用.In order to further reveal the internal relationship between the symmetry of nonholonomic systems and the conserved quantities,the Mei symmetry of nonholonomic systems and its conserved quantities based on fractional order models were proposed and studied.Firstly,according to the fractional d'Alembert-Lagrange principle,the dynamic equations of nonholonomic systems based on fractional models are established.Secondly,according to the invariance that the dynamic functions in the dynamic equations are still consistent with the original equations after infinitesimal transformation,the Mei symmetry theorem of nonholonomic systems under fractional models is established,and the conserved quantities of Mei-type are given.Thirdly,the Mei symmetry theorems of fractional Hamilton systems,nonholonomic systems based on integer order models and fractional Lagrange systems with nonholonomic constraints are discussed.Finally,the applicability of the obtained results is illustrated through an example.

关 键 词：非完整系统 MEI对称性 MEI守恒量 分数阶模型 

分 类 号：O316[理学—一般力学与力学基础]