  Following on from our previous study of the geodesic flow on three
dimensional ellipsoid with equal middle semi-axes, here we study the remaining
cases: Ellipsoids with two sets of equal semi-axes with $SO(2) \times SO(2)$
symmetry, ellipsoids with equal larger or smaller semi-axes with SO(2)
symmetry, and ellipsoids with three semi-axes coinciding with SO(3) symmetry.
All of these cases are Liouville-integrable, and reduction of the symmetry
leads to singular reduced systems on lower-dimensional ellipsoids. The critical
values of the energy-momentum maps and their singular fibers are completely
classified. In the cases with SO(2) symmetry there are corank 1 degenerate
critical points; all other critical points are non-degenreate. We show that in
the case with $SO(2) \times SO(2)$ symmetry three global action variables exist
and the image of the energy surface under the energy-momentum map is a convex
polyhedron. The case with SO(3) symmetry is non-commutatively integrable, and
we show that the fibers over regular points of the energy-casimir map are $T^2$
bundles over $S^2$.
