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

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.