  We have developed a new formulation to obtain self-gravitating, axisymmetric
configurations in permanent rotation. The formulation is based on the
Lagrangian variational principle, and treats not only barotropic but also
baroclinic equations of state, for which angular momentum distributions are not
necessarily cylindrical. We adopt a Monte Carlo technique, which is analogous
to those employed in other fields, e.g. nuclear physics, in minimizing the
energy functional, which is evaluated on a triangulated mesh. This letter is a
proof of principle and detailed comparisons with existing results will be
reported in the sequel, but some test calculations are presented, in which we
have achieved an error of $O(10^{-4})$ in the Virial relation. We have in mind
the application of this method to two-dimensional calculations of the
evolutions of rotating stars, for which the Lagrangian formulation is best
suited.
