Classical Mechanics · Rigid bodies and rotating frames
Principal axes of a coupled planar inertia tensor
Problem
A rigid body has inertia tensor $\mathbf I=I_0\begin{pmatrix}4&-\sqrt3&0\\-\sqrt3&2&0\\0&0&5\end{pmatrix}$ in an orthonormal body basis. Find all principal moments and an orthonormal principal-axis basis. Identify any degeneracy and explain the resulting freedom of principal axes.
Hint
Diagonalize the symmetric planar block and keep the already decoupled $z$ direction.
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