  In two papers we proposed a continuum model for the dynamics of systems of
self propelling particles with kinematic constraints on the velocities and
discussed some of its properties. The model aims to be analogous to a discrete
algorithm used in works by T. Vicsek et al. In this paper we derive the
continuous hydrodynamic model from the discrete description. The similarities
and differences between the resulting model and the hydrodynamic model
postulated in our previous papers are discussed. The results clarify the
assumptions used to obtain a continuous description.
