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

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- Solution d

Solution

With compatible signs,

ω_{2} = A tanh (Ω t), ω_{3} = Ω sech (Ω t) .

Thus as $t \to \infty$ , $ω_{1}$ and $ω_{3}$ vanish while $ω_{2} \to A$ . The body approaches steady rotation about the intermediate principal axis; the full separatrix connects the two opposite intermediate-axis rotations.

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