机械多体系统碰撞动力学的对称性和守恒量研究  

Study on Symmetries and Conserved Quantities of Mechanical Multibody System Collision Dynamics

作　　者：郑明亮 冯鲜[1] 李文霞[1] 曹亚玲[1] ZHENG Mingliang;FENG Xian;LI Wenxia;CAO Yalin(Wuxi Taihu University,Wuxi,Jiangsu 214054,P.R.China)

机构地区：[1]无锡太湖学院,江苏无锡214064

出　　处：《应用数学和力学》2018年第11期1292-1299,共8页Applied Mathematics and Mechanics

基　　金：江苏省高等学校自然科学基金(18KJB460027)

摘　　要：为给复杂机械多体系统碰撞动力学问题的定量和定性分析提供一个强有力新工具,该文将现代分析力学中的对称性理论引入到机械多体外碰撞动力学研究中.首先,基于冲量动量法推导系统碰撞动力学的Euler-Lagrange方程;其次,引进群分析理论,根据不变性原则给出系统存在Noether对称性与Lie对称性的各自条件方程以及得到相应守恒量的形式,为动力学方程的解析积分理论提供了有效途径.最后以一平面开环两连杆机构的碰撞力学为例进行实际分析运用.研究表明,借助对称性和守恒量可以得到机械多体系统动力学更深层次的力学规律和运动特性,可为系统更精确的动态优化设计和先进控制奠定理论基础.To provide a powerful new tool for quantitative and qualitative analysis of collision dynamics in complex mechanical multibody systems, the symmetry theory in modern analytical mechanics was introduced into the study of mechanical multibody external collision dynamics. Firstly, the Euler-Lagrange equation of collision dynamics was derived based on the momentum method; secondly, the group theory was introduced, then, according to the invariance principle, the condition equations for the Noether symmetry and the Lie symmetry were obtained and the corresponding conserved quantity form was got, which made possible an effective approach to the analytic integral theory for dynamic equations. Fnally, the collision dynamics of a planar open-loop 2-connecting-rod mechanism was taken as an example for application and analysis. Research shows that deeper mechanical laws and motion characteristics of mechanical multibody system collision dynamics can be obtained by means of symmetries and conserved quantities, and the results also lay a theoretical foundation for more precise dynamic optimal design and advanced control.

关 键 词：机械多体系统 EULER-LAGRANGE方程 对称性 守恒量 平面连杆 

分 类 号：TH122[机械工程—机械设计及理论] O316[理学—一般力学与力学基础]