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前述结论及其具体应用方式。
Abstract
Based on the theory of analytical mechanics and the basic principle of dynamics, the collision problem solution methods of rigid body were generalized and extended. Starting from the integral form of the momentum theorem, the inertial impulse was introduced, then the dynamic-static method for collisions was obtained by analogy with the d'Alembert principle. Furthermore, combined with the virtual work principle, the d'Alembert-Lagrange equation of collisions was derived, which simplified the analysis process of multi-constraint and multi-rigid body mechanism collision problems. By integrating Lagrange equation in arbitrary time period of collision, the relation between arbitrary instantaneous velocity of a system and impulse of collision was established, and the Lagrange equation of state expressed by relative kinetic energy was derived by differential operation, whose form is simple and innovative. Finally, several typical examples were given to verify the above conclusion and deduce their specific application.
关键词
碰撞；惯性冲量；碰撞的d&rsquo /
Alembert-Lagrange方程；相对动能；碰撞Lagrange方程
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Key words
collision /
inertial impulse /
d'Alembert-Lagrange equation for collisions /
relative kinetic energy /
Lagrange equation for collisions
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