Impact Dynamics of Multibody Systems Based on Kane's Equations

基於凱恩方程之多體系統衝擊動力學研究

衝擊運動起因於系統受衝擊力或衝擊約束。本文應用凱恩方程研究多體系統衝擊動力學，系統的運動分成衝擊前、衝擊、衝擊後三段區間。將廣義力、廣義慣性力及廣義拘束力投影到偏速度及偏角速度後積分，再應用休士頓運動程序可得到多體系統衝擊動力方程。最後用數個例題來驗證運動方程的正確性及展示系統衝擊前後的運動情形。

Impulsive motion arises from a system subjected to applied impulsive forces or subjected to impulsive constraints. This paper uses Kane’s equations to study impact dynamics of multibody systems. The impulsive motion can be divided into pre-impact, impact and post-impact intervals. By projecting the integrals of generalized active forces, generalized inertia forces and generalized constraint forces along the partial angular velocities and partial velocities, the impact dynamical equations may then be obtained using Huston’s kinematics procedure. The examples validate the dynamical equations and demonstrate the pre-impact and post-impact motion of the systems.