Conversion between Cartesian and Cylindrical coordinates. HOW??????

Question

Conversion between Cartesian and Cylindrical coordinates.  HOW??????

thomas5267 · Answer

I need to convert a simplified Navier-Stokes to cylindrical coordinates.

Wikipedia gives this:
$$
\begin{bmatrix}\mathbf{\hat r} \ \boldsymbol{\hat\theta} \ \mathbf{\hat z}\end{bmatrix}
  = \begin{bmatrix} \cos\theta & \sin\theta & 0 \
                   -\sin\theta & \cos\theta & 0 \
                   0 & 0 & 1 \end{bmatrix}
$$
but this makes no sense whatsoever.

thomas5267 · Answer

@ikram002p Help!  I have been stuck on this weird thing for a day now.

thomas5267 · Answer

Took the formula from this link. https://en.wikipedia.org/wiki/Vector_fields_in_cylindrical_and_spherical_coordinates#Cylindrical_coordinate_system

thomas5267 · Answer

@ParthKohli @ganeshie8 @perl

thomas5267 · Answer

I will check the answer at 00, 15, 30, 45 minute since I spilled a whole cup of water on my notebook on Sunday.  I am now using my iPad and the notebook is now drying.  iPad isn't famous for is multitasking ability lol.  I do not have the courage to reassemble it and turn it back on only to electrocute my computer due to incomplete drying.