 Solution

ID: past-exam-of-the-classical-mechanics-course-of-the-university-of-oxford/2023/3/b/i/solution

p = \partial L_{0} / \partial \overset{q}{˙} = m \overset{q}{˙}

. Substituting

\overset{q}{˙} = p / m

p = m \overset{q}{˙}, H_{0} (q, p) = p \overset{q}{˙} - L_{0} = \frac{p ^{2}}{2 m} + \frac{m ω ^{2} q ^{2}}{2} .

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