Algebraic solutions and computational strategy for planar multibody systems subjected to impact with friction

Abstract

This paper presents a precise and effective formulation for modeling and simulating impact with friction for planar multibody systems. Nonlinear equations of motion are formulated using normal impulse at contact point as a time-like independent variable. The derived equations demonstrate that sliding during impact period could persist, or it could cease leading either to a persistence of sticking or to a reverse sliding. To distinguish between these different modes, Routh’s incremental method is employed. A critical coefficient of friction, dependent solely on the system configuration, is identified and used to determine whether the contact mode is sliding or sticking. Three definitions of coefficient of restitution are introduced to model the plasticity of the impact. Analytical algebraic solutions and a computational strategy are offered to identify the mode of impact and to evaluate the impact variables. An example is thoroughly examined to demonstrate the effectiveness of the formulation, validate the algebraic solutions, and evaluate the outcomes of the three definitions of the coefficient of restitution.