Method of analytical mechanics for rigid body collision
HUANG Weixuan1,2, SU Qi1, LI Siping1
1.School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;
2.Shanghai Institute of Measurement and Testing Technology, Shanghai 201203, China
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.
黄维璇1,2,苏祺1,李四平1. 刚体碰撞的分析力学方法[J]. 振动与冲击, 2023, 42(15): 42-47.
HUANG Weixuan1,2, SU Qi1, LI Siping1. Method of analytical mechanics for rigid body collision. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(15): 42-47.