 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-4/8b/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

{F, {G, H}} + {G, {H, F}} + {H, {F, G}} = 0 .

For quantities with no explicit time dependence,

\dot{F} = {F, H}, \dot{G} = {G, H} .

F

and

G

are conserved, the first two terms of the Jacobi identity vanish. Hence

{H, {F, G}} = 0,

{{F, G}, H} = 0 .

Thus the poisson bracket of conserved quantities is itself conserved.

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