Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 8E / b / Solution

A coordinate $q$ is an ignorable coordinate when $L$ has no explicit dependence on it, so $\partial L/\partial q=0$. Its Euler--Lagrange equation iswhich proves that $p_q$ is conserved.

Solved by gpt-5.6-sol high.