 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-4/15d/b/solution

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

To first order the conditions are

\partial_{p_{j}} δ q_{i} - \partial_{p_{i}} δ q_{j} = 0

\partial_{q_{j}} δ p_{i} - \partial_{q_{i}} δ p_{j} = 0

, and

\partial_{q_{j}} δ q_{i} + \partial_{p_{i}} δ p_{j} = 0

δ q_{i} = ε F_{p_{i}}

and

δ p_{i} = - ε F_{q_{i}}

satisfy them by equality of mixed partials.

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