  A simple rearrangement of the torque free motion Hamiltonian shapes it as a
perturbation problem for bodies rotating close to the principal axis of maximum
inertia, independently of their triaxiality. The complete reduction of the main
part of this Hamiltonian via the Hamilton-Jacobi equation provides the
action-angle variables that ease the construction of a perturbation solution by
Lie transforms. The lowest orders of the transformation equations of the
perturbation solution are checked to agree with Kinoshita's corresponding
expansions for the exact solution of the free rigid body problem. For
approximately axisymmetric bodies rotating close to the principal axis of
maximum inertia, the common case of major solar system bodies, the new approach
is advantageous over classical expansions based on a small triaxiality
parameter.
