 Steady precession quadratic for an orientation-dependent potential

For an axially symmetric rotational Lagrangian with potential $Mgh\cos \theta$, fixed tilt and conservation of the spin and azimuthal momenta give constant precession. The tilt equation becomes $A{\Omega }^2\cos \alpha -Cn\Omega +Mgh=0$. A real precession rate requires the quadratic discriminant to be nonnegative. The inertia and height parameters must correspond consistently to the chosen fixed point.