 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ii/paper-3/8d/b/solution

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

\frac{df}{d t} = \sum_{i = 1}^{3} (\frac{\partial f}{\partial q _{i}} \overset{q}{˙}_{i} + \frac{\partial f}{\partial p _{i}} \overset{p}{˙}_{i}) = \sum_{i = 1}^{3} (\frac{\partial f}{\partial q _{i}} \frac{\partial H}{\partial p _{i}} - \frac{\partial f}{\partial p _{i}} \frac{\partial H}{\partial q _{i}}) = {f, H} .

f is conserved ⟺ {f, H} = 0.

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