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

If $f$ has no explicit $y$ dependence, the Euler-Lagrange equation becomes $d(f_{y^{\prime }})/dx=0$. ThusThe variable $y$ is then a cyclic coordinate. This is the case used for the azimuth in the ramp calculation.