Linear stability of principal-axis rotation

Linearize the Euler equations for a torque-free rigid body about rotation with angular speed $\Omega$ along the third principal axis. The transverse perturbations obeyand henceCyclic permutation gives the corresponding equations about the other two axes. For $I_1<I_2<I_3$, the squared frequency is positive about axes one and three, whereas the intermediate-axis equation has a positive exponential-growth coefficient.