  This paper is concerned with the problem of an ellipsoid of revolution
rolling on a horizontal plane under the assumption that there is no slipping at
the point of contact and no spinning about the vertical. A reduction of the
equations of motion to a fixed level set of first integrals is performed.
Permanent rotations corresponding to the rolling of an ellipsoid in a circle or
in a straight line are found. A linear stability analysis of permanent
rotations is carried out. A complete classification of possible trajectories of
the reduced system is performed using a bifurcation analysis. A classification
of the trajectories of the center of mass of the ellipsoid depending on
parameter values and initial conditions is performed.
