 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2008/h/h1/ii/solution

E = \sum_{a} \overset{q}{˙}_{a} \partial L / \partial \overset{q}{˙}_{a} - L

. Along a solution,

\frac{d E}{d t} = \sum_{a} \overset{q}{˙}_{a} (\frac{d}{d t} \frac{\partial L}{\partial q ˙ _{a}} - \frac{\partial L}{\partial q _{a}}) - \frac{\partial L}{\partial t} = - \frac{\partial L}{\partial t} .

E = a \sum \overset{q}{˙}_{a} \frac{\partial L}{\partial q ˙ _{a}} - L .

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