 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-1/9/ii/a/solution

When

F_{y} = 0

, the Euler-Lagrange equation reduces immediately to

d F_{y^{'}} / d x = 0

. Therefore

F_{y^{'}} = C .

This is conservation of the generalized momentum associated with a cyclic coordinate.

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