  A general method is presented for constructing distribution functions for
flat systems whose surface density and Toomre's Q number profile is given. The
purpose of these functions is to provide plausible galactic models and assess
their critical stability with respect to global non axi-symmetric modes. The
derivation may be carried out for an azimuthal velocity distribution (or a
given specific energy distribution) which may either be observed or chosen to
match a specified temperature profile. Distribution functions describing stable
models with realistic velocity distributions for power law disks, the Isochrone
and the Kuzmin disks are provided. Specially simple inversion formulae are also
given for finding distribution functions for flat systems whose surface
densities are known.
