Complementarity problems in multibody systems with planar friction

Abstract

In multibody dynamics, topology variations are caused by the fact that bodies, that are initially separated from one another, get into contact and slide or roll along each other under the influence of friction. These topology variant systems are characterized by the fact that, during the evolution in time, their number of degrees of freedom changes by latent constraints becoming active or passive due to and controlled by the system dynamics itself. In studying such systems, the following procedure is selected: With a system description in minimal coordinates without use of latent constraints, the constraints that are indicated as being potentially active by the evaluation of kinematic indicators, in this case being relative velocity and distance, are considered as algebraic secondary conditions and are taken into account by including Lagrange multipliers in the equation of motion. A sufficient condition for all potentially active constraints to remain active or become passive is provided by the solution of a complementarity problem that, in a planar case, is linear and argues at acceleration level by self-excluding kinetic indicators.