Lagrange top

A Lagrange top is an axisymmetric rigid body with one point fixed on its symmetry axis, moving in a uniform gravitational field with its center of mass on that axis.

For a Lagrange top whose inclination $\theta$ is measured from the upward vertical, steady precession at angular speed $\Omega$ obeysThus steady precession at a prescribed $0<\theta <\pi /2$ exists precisely when