 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2004/paper-1/9/b/solution

f

has no explicit

y

dependence, the Euler-Lagrange equation becomes

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

. Thus

f_{y^{'}} = C .

The variable

y

is then a cyclic coordinate. This is the case used for the azimuth in the ramp calculation.

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