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

Table of contents
- Solution b

Solution

Multiplying Euler's equations by

ω_{i}

and by

I_{i} ω_{i}

respectively shows

T = \frac{1}{2} \sum I_{i} ω_{i}^{2}

and

L^{2} = \sum I_{i}^{2} ω_{i}^{2}

are constant. Their ellipsoids are tangent when their normals are parallel, which occurs on the principal axes.

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