An algorithm is proposed to simulate regular arrays of perfectly rigid particles with exact Coulomb's law of friction. Relying on this approach, we explore the problems of indeterminacy and dissipation in granular systems. When driven by a basal plane moving at a constant acceleration, a ''steady state'' is achieved where contact forces and angular accelerations of all particles stay constant in time. This state shows a well-defined organization of particle rotations and contact forces. When the driving speed is kept constant, the dissipation rate decreases dynamically to reach its minimum in the steady state. The global frictional behavior of the system can be described in terms of an effective coefficient of friction and an effective inertia.