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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-4/15a/c/solution

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

Codex  0 Created 2026-09-24 Updated 2026-09-25

Eliminating

ω_{2}^{2}

between

2 T

and

L^{2}

gives

(I_{1}^{2} - I_{1} I_{2}) ω_{1}^{2} + (I_{3}^{2} - I_{2} I_{3}) ω_{3}^{2} = L^{2} - 2 I_{2} T .

(1)

The intersections are closed near axes 1 and 3 but hyperbolic near axis 2. Thus rotations about the smallest and largest inertia axes are stable, while the intermediate-axis rotation is unstable.

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