Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 2 / 14B / c / Solution

When $a=b<c$, the ellipsoid is an axisymmetric rigid body withThe angle between its symmetry axis and the fixed angular momentum is constant. In an inertial frame the symmetry axis precesses uniformly around $\mathbf{L}$, while the body simultaneously spins about that axis. The angular-velocity vector also traces a circular cone about $\mathbf{L}$. The limiting cases are pure rotation about the symmetry axis and pure rotation about a perpendicular principal axis.