Phase modelling of spherical stellar systems having ellipsoidal distribution of velocities.

The possibility of phase modelling of selfgravitating stellar spherical systems with ellipsoidal distribution of velocities is considered. For this purpose the gravitational potential of a system was represented in the form that was proposed by Kuzmin and Malasidze (1970). The phase density function is given as a solution of Abel-type integral equation. An expression of the radial velocity dispersion is obtained. It is also established that by proper choice of potential and velocity spatial anisotropy parameters the Kuzmin-Veltman model with radially aligned ellipsoidal dispersion of velocities and also the classical Eddington model of spherical distribution of velocities can be obtained.