  We analyse the motion of a sphere that rolls without slipping on a conical
surface having its axis in the direction of the constant gravitational field of
the Earth. This nonholonomic system admits a solution in terms of quadratures.
We exhibit that the only circular of the system orbit is stable and furthermore
show that all its solutions can be found using an analogy with central force
problems. We also discuss the case of motion with no gravitational field, that
is, of motion on a freely falling cone.
