Three-dimensional impact with friction

For solving 3D impacts with friction a numerical integration method is developed in this paper. Using Coulomb's Frictional Law and with the hypothesis of invariant configuration of the systems during impact, two sets of differential equations governing the impact process are built up in impulse space based on the Lagrangian equation. The coefficient of restitution defined by Poisson is used to denote the end of impact. The singular cases of tangential movement at sticking point are especially considered. The direction of resumption of sliding motion at sticking point can be determined by a searching arithmetic. It is verified that there is one and only one invariant direction existing out of the sticking point.