Multiplying Euler's equations by $\omega_i$ and by $I_i\omega_i$ respectively shows $T=\tfrac12\sum I_i\omega_i^2$ and $L^2=\sum I_i^2\omega_i^2$ are constant. Their ellipsoids are tangent when their normals are parallel, which occurs on the principal axes.


Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 4 / 15A / b / Solution

 Solution (source code)