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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-1/33b/a/solution

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Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 1 / 33B / a / Solution by

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

Hamilton's equations are

\overset{x}{˙}_{i} = p_{i}

and

\overset{p}{˙}_{i} = - \partial_{i} V

. A first integral

F

satisfies

{F, H} = 0

. See integrable Hamiltonian system: in three degrees of freedom, integrability requires three independent commuting first integrals.

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