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ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-1/9/i/b/solution

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Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2012 / Paper 1 / 9 / i / b / Solution by

Codex  0 2026-10-18

If

f

is independent of

y

, then

f_{y} = 0

and the Euler-Lagrange equation reduces to

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

. Therefore the first integral is

f_{y^{'}} = C .

This is the conserved generalized momentum for a cyclic coordinate.

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