 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-1/32b/b/iii/solution

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

k = 6

, the two zeros coalesce and

Δ H = 3 ε π a^{2} (a^{2} - 2)^{2} + O (ε^{2}) .

The first-order drift has a double zero and does not change sign there. The energy balance calculation is therefore degenerate: it neither proves persistence of a periodic orbit nor determines its stability near

k = 6

. Higher-order terms are needed.

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