刚体碰撞的分析力学方法  

Method of analytical mechanics for rigid body collision

作　　者：黄维璇 苏祺 李四平[1] HUANG Weixuan;SU Qi;LI Siping(School of Naval Architecture,Ocean&Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China;Shanghai Institute of Measurement and Testing Technology,Shanghai 201203,China)

机构地区：[1]上海交通大学船舶海洋与建筑工程学院,上海200240 [2]上海市计量测试技术研究院,上海201203

出　　处：《振动与冲击》2023年第15期42-47,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金面上项目(51878407)。

摘　　要：从分析力学思想和动力学基本原理出发,对刚体为主的质点系碰撞问题解法进行系统归纳和拓展延伸。从动量定理的积分形式引入惯性冲量,类比D’Alembert原理得到求解碰撞问题的动静法,进一步结合虚功原理推导了碰撞问题的D’Alembert-Lagrange方程,简化了多约束、多刚体的机构碰撞问题的分析过程。将Lagrange方程在任意碰撞时程内积分,建立了在碰撞任意瞬时系统速度与碰撞冲量间的关系,并经微分运算推导出相对动能表达的Lagrange状态方程,形式简洁新颖。最后的实例验证和演绎了该结论及其具体应用方式。Here,starting from the theory of analytical mechanics and basic principles of dynamics,solving methods for collision problem of mass-point system dominated by rigid body were systematically summarized and extended.Inertia impulse was introduced from the integral form of momentum theorem,and the dynamic and static method for solving collision problems was obtained through analogy to D’Alembert principle.D’Alembert-Lagrange equation of collision problem was further derived by combining the virtual work principle to simplify analysis processes of collision problems of mechanisms with multi-constraint and multi-rigid body.By integrating Lagrange equations within any collision time history,relations between system velocities and collision impulses at any collision instant were established,Lagrange state equations expressed using relative kinetic energy with simple and novel forms were derived through differential operations.Finally,examples verify and deduce the above conclusions and their specific application patterns.

关 键 词：碰撞 惯性冲量 碰撞的D’Alembert-Lagrange方程 相对动能 碰撞Lagrange方程 

分 类 号：O313.4[理学—一般力学与力学基础]