Solution
= Solution
Eliminating $\omega_2^2$ between $2T$ and $L^2$ gives
$$
(I_1^2-I_1I_2)\omega_1^2+(I_3^2-I_2I_3)\omega_3^2=L^2-2I_2T.
$$
The intersections are closed near axes 1 and 3 but hyperbolic near axis 2. Thus rotations about the smallest and largest inertia axes are stable, while the intermediate-axis rotation is unstable.