A method for the numerical integration of mechanical systems with unilateral constraints: study of impact in multibody systems

Abstract

Study of mechanical systems with unilateral constraints is associated with forming two systems of equations, a system of differential equations and a system of algebraical equations. Differential equations are used to describe the motion until the moment of impact, i.e. until activation of unilateral constraints. Algebraic equations are used to describe the impact. During numerical integration, transition from one system to another occurs at the points of impact. Even in simple problems, forming algebraic equations represents a complex task. This paper presents a method, the so-called Reduction Method, which provides for the analysis of these systems without forming the algebraic equations. They are substituted by a new system which is easily derived from equations of motion. Compared to methods based on the classical impact theory, using Reduction Method,velocities after the impact are easily computed regardless of the degrees of freedom.