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Past exam of the physics 1 paper of the University of Oxford / 2019 / 9 / a / Solution Created 2026-10-25 Updated 2026-11-05

For a Lagrangian

L (q_{i}, \overset{q}{˙}_{i}, t)

expressed in independent generalized coordinates, stationary action gives the Euler-Lagrange equations

\frac{d}{d t} \frac{\partial L}{\partial q ˙ _{i}} - \frac{\partial L}{\partial q _{i}} = 0.

Ideal constraints can either be incorporated into the independent coordinates or treated using Lagrange multipliers, as in solution.

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