Impact of a multiple pendulum with a non-linear contact force

Abstract

This article presents a method to solve the impact of a kinematic chain in terms of a non-linear contact force. The nonlinear contact force has different expressions for elastic compression, elasto-plastic compression, and elastic restitution. Lagrange equations of motion are used to obtain the non-linear equations of motion with friction for the collision period. The kinetic energy during the impact is compared with the pre-impact kinetic energy. During the impact of a double pendulum the kinetic energy of the non-impacting link is increasing and the total kinetic energy of the impacting link is decreasing.