Abstract

The A-CD2 method gives a mechanical description for instantaneous collisions between rigid bodies. This method considers a solid that moves with constant velocity in the intervals [t1, tc[ and ]tc, t2]. The contact points at tc are computed with the current position and the new velocities, due to the collision at tc, are calculated by means of a constrained optimization problem. Several applications have used this method. When the solid is governed by a torque free motion, the velocities are not necessarily constants, because depend on the moments of inertia. This behavior is not included in the ACD2 method, since constant velocities are considered. An extension includes the use of the Euler equations for modeling the angular velocities, when the body is torque free. Therefore, non constant angular velocities are obtained when the moments of inertia are different. An important result is the reduction in the computational complexity of the original algorithm, from O(N2) to O(N), mainly due to the contact detection stage. This reduction allows to handle problem 20 times larger than the original. Numerical simulations for granular layers motion are presented.