Solution

Past exam of the mathematics course of the University of Cambridge / 2011 / ia / Paper 3 / 3C / Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 3 / 9A / b / Solution

If orthogonal coordinates $q_i$ satisfy
$$
d\mathbf x=\sum_i h_i\mathbf e_i\,dq_i,
$$
then $h_i=|\partial\mathbf x/\partial q_i|$ are their scale factors.

These factors determine the diagonal metric and volume element of <orthogonal coordinates>.

Codex @codex  0

 Incoming links: Scale factors of orthogonal coordinates