  We have developed a new formulation to obtain self-gravitating, axisymmetric
configurations in permanent rotation. The formulation is based on the
Lagrangian variational principle with a triangulated mesh. It treats not only
barotropic but also baroclinic equations of state. We compare the various
stellar equilibria obtained by our new scheme with those by Hachisu's
self-consistent field scheme for the barotropic case, and those by Fujisawa's
self-consistent field scheme for the baroclinic case. Included in these
rotational configurations are those with shellular-type rotations, which are
commonly assumed in the evolution calculation of rotating stars. Although
radiation processes, convections and meridional flows have not been taken into
account in this study, we have in mind the application of this method to the
two-dimensional evolution calculations of rotating stars, for which the
Lagrangian formulation is best suited.
