 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2011/ii/paper-4/9c/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

{f, g} = i \sum (\frac{\partial f}{\partial q _{i}} \frac{\partial g}{\partial p _{i}} - \frac{\partial f}{\partial p _{i}} \frac{\partial g}{\partial q _{i}}) .

\overset{q}{˙}_{i} = H_{p_{i}}

and

\overset{p}{˙}_{i} = - H_{q_{i}}

in the chain rule yields

\frac{df}{d t} = \frac{\partial f}{\partial t} + {f, H} .

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