 Solution

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

A coordinate absent from the Lagrangian is cyclic. Its Euler-Lagrange equation gives

\frac{d}{d t} \frac{\partial L}{\partial q ˙ _{1}} = \frac{\partial L}{\partial q _{1}} = 0.

Thus the corresponding generalized momentum

p_{1} = \partial L / \partial \overset{q}{˙}_{1}

is conserved.

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