  We construct models of rotating stars using the perturbative approach
introduced by J. Hartle in 1967, and a set of equations of state proposed to
model hadronic interactions in the inner core of neutron stars. We integrate
the equations of stellar structure to third order in the angular velocity and
show, comparing our results to those obtained with fully non linear codes, to
what extent third order corrections are needed to accurately reproduce the
moment of inertia of a star which rotates at rates comparable to that of the
fastest isolated pulsars.
