Generalized theory of impacts in particulate systems

The theory of collisional systems is generalized for an arbitrary geometry and forces acting in the system, mixtures of different particle types, friction, small deviations from the ideal spherical form, axial rotation, finite size of particles and gravitational interactions. Terms for the formation of new particles and destruction of old ones are also included, and other unspecified parameters can be introduced. Although some approximations are made to simplify the basic equations and to avoid excessive numerical interactions, a comparison with computer simulations shows a good agreement. The tests were continued up to the optical thickness = 5.