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

The initial relation implies $L^2=2I_{2}T$, and conservation preserves it. With $I_3=I_1+I_2$, this identity reduces toThe energy then givesThe first Euler equation is ${\dot{\omega }}_1=-{\omega }_2{\omega }_3$. Squaring and substituting the preceding identities yields