Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 15E / a / Solution

The kinetic energy and squared angular-momentum magnitude areDifferentiate and substitute Euler's equations. In $\dot{T}$, the coefficient of ${\omega }_1{\omega }_2{\omega }_3$ isThe analogous weighted sum in $d{L}^2/dt$ also cancels, so both quantities are conserved.