All across literature and the web one can find formulae, e.g. for converting cartesian to polar coodrinates or for translation and rotation in cartesian coordinates.
But recently I ran into the problem of requiring a two dimensional integral in polar coordinates due to some radial symmetry. Unfortunately within this symmetry I have another but linearly displaced radial symmetry. In order to perform the integral I had to find a formuale for describing the linear translation in polar coordinates.
Nowhere in the web I found a formula. So I had to derive an expression from the linear translation vector in cartesion coordinates and convert that one to polar coordinates.