Analysis of Some Difficulties Encountered in the Simulation of Mechanical Systems with Constraints

摘要

Mathematical properties of mechanical systems of rigid bodies with constraints are investigated. In particular, properties of interest for the digital simulation of such systems are studied. Much attention is paid to normal and friction forces in planar systems. The main mathematical tool is the theory of linear complementarity problems. Problems where the constraints give rise to normal forces only are found to be much simpler than those with Coulomb friction. For systems exposed to friction, solutions may fail to exist and if they do exist, they need not be unique. The related question of how to compute impulses, e.g., after a collision, is treated briefly.