Non-homogeneous axisymmetric models of self-gravitating systems: the numerical matching

Non homogeneous axisymmetric models of self-gravitating systems are discussed by using functional methods and numerical techinques. More in detail, in a reference frame, rotating with constant angular velocity Omega, a self-gravitating incompressible fluid, in steady state is considered. In particular the internal velocity field has flow lines normal to the global angular velocity. Deriving a generalized Lane-Emden equation and using a procedure inspired by the method of Eriguchi-Muller, for selected velocity profiles, a sequence of equilibrium configurations is found and discussed.