My name is Alexander FufaeV and here I write about:
Cylinder Coordinates
The cylindrical coordinates are a coordinate system. It is particularly useful when dealing with problems that have cylindrical symmetry. The cylindrical coordinate system consists of three main components: the radial \( \class{red}{r_{\perp}} \), azimuthal \( \class{green}{\varphi} \) and vertical \( \class{blue}{z} \) coordinates.
$$ \begin{align} \begin{bmatrix} x\\y\\z \end{bmatrix}~=~\begin{bmatrix} \class{red}{r_{\perp}}\,\cos(\class{green}{\varphi}) \\\ \class{red}{r_{\perp}}\,\sin(\class{green}{\varphi})\\\class{blue}{z}\end{bmatrix} \end{align} $$