The numerical method for three-dimensional impact with friction of multi-rigid-body system  

作　　者：ZHAO Zhen1,2, LIU Caishan2 & CHEN Bin2 1. Beijing Institute of Graphic Communication, Beijing 102600, China 2. Department of Mechanics & Engineering Science, Peking University, Beijing 100871, China 

出　　处：《Science China(Physics,Mechanics & Astronomy)》2006年第1期102-118,共17页中国科学：物理学、力学、天文学（英文版）

基　　金：the National Natural Science Foundation of China (Grant Nos. 10272002, 10502009 , 60334030); the Natural Science Foundation of Beijing (Grant No. 1062007).

摘　　要：The differential equations for planar impacts reduce to an algebraic form, and can be easily solved. For three dimensional impacts with friction, there is no closed-form solution, and numerical integration is required due to the swerve behavior of tangential impulse during collisions. The dynamic governing equations in the impact process are built up in impulse space based on the Lagrangian equation in this paper. The coefficient of restitution defined by Poisson is used as the condition of impact termination. A valid nu- merical method for solving three-dimensional frictional impact of multi-rigid body system is established. The singular cases of tangential movement in sticking point are especially noticed and analyzed. Several examples are present to reveal the different kinds of tan- gential movement modes varied with the normal impulse during collision.The differential equations for planar impacts reduce to an algebraic form, and can be easily solved. For three dimensional impacts with friction, there is no closed-form solution, and numerical integration is required due to the swerve behavior of tangential impulse during collisions. The dynamic governing equations in the impact process are built up in impulse space based on the Lagrangian equation in this paper. The coefficient of restitution defined by Poisson is used as the condition of impact termination. A valid nu- merical method for solving three-dimensional frictional impact of multi-rigid body system is established. The singular cases of tangential movement in sticking point are especially noticed and analyzed. Several examples are present to reveal the different kinds of tan- gential movement modes varied with the normal impulse during collision.

关 键 词：multi-rigid body  impact  friction. 

分 类 号：O313.4[理学—一般力学与力学基础]