 Solution

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

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

(0, Ω, 0)

gives

\overset{u}{˙} = - A v

\overset{v}{˙} = - B u

, where

A = (I_{3} - I_{2}) Ω/ I_{1}

B = (I_{2} - I_{1}) Ω/ I_{3}

. With

κ = A B

u = u_{0} cosh κ t - (A / κ) v_{0} sinh κ t, q u a d v = v_{0} cosh κ t - (B / κ) u_{0} sinh κ t .

The exponential growth confirms intermediate-axis instability.

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