Explain how the orientation of a rigid body can be specified by means of the three Eulerian angles, $\theta, \phi$ and $\psi$.

An axisymmetric top of mass $M$ has principal moments of inertia $A, A$ and $C$, and is spinning with angular speed $n$ about its axis of symmetry. Its centre of mass lies a distance $h$ from the fixed point of support. Initially the axis of symmetry points vertically upwards. It then suffers a small disturbance. For what values of the spin is the initial configuration stable?

If the spin is such that the initial configuration is unstable, what is the lowest angle reached by the symmetry axis in the nutation of the top? Find the maximum and minimum values of the precessional angular velocity $\dot{\phi}$.