Cylindrical Coordinates

Projection onto $xy$ plane is just polar coordinates

$(x,y,z)=(r\cos \theta ,r\sin \theta ,z)$

• Conversion from cylindrical coordinates to rectangular coordinates

$(r,\theta ,z)=\left(\sqrt{x^2+y^2},{\tan }^{-1}\left(\frac{y}{x}\right),z\right)$

• Conversion from rectangular to cylindrical coordinates

$J_{\text{polar}}=J_{\text{cylindrical}}=r$