Modeling and simulating of planar multi-body systems with rolling resistance and Coulomb friction

To study the planar multi-body systems with rolling resistance and Coulomb friction, the generalized mechanics model with a number of rigid bodies and disks was established and the dynamical equations of the system were derived from Lagrange-s equations of the first kind in Cartesian coordinate. In order to compute constraint forces, constraint equations of the system were expressed by local approach and the generalized forces of rolling resistance couples and Coulomb friction forces were given in the matrix notation. The complementarity conditions of the rolling resistance law and the reaction forces of the hinge were formed to solve the non-smooth differential equations. A constraint-stabilized event-driven method for the system was given. So the problems of the computation for non-smooth forces and the reaction forces of the hinge and the judgment for the stick-slip were transformed into a linear complementarity problem. The disk and the planar rigid multi-body system with rolling resistance and Coulomb friction were respectively considered as demonstrative application examples and numerical results were presented.