How Do Cartesian Components Transform into Cylindrical Coordinates?

[od7]

Hi.

I’ve just started learning about tensors on my own and am still trying to understand coordinate transformations.

If I begin with a vector whose Cartesian components are (x, y, z) and apply the tensor transformation to cylindrical polars, I end up with (r, 0, z) – is this right? I anticipated (r, phi, z) – have I made an error or am I not understanding something?

Please help!

 

[mathwonk]

i am not sure what you are doing, but it seems fishy to go from three variables to two. i.e. from a description of three space, to a description of a piece of the plane

 

[robphy]

It seems you wish to write a vector \vec V
given in rectangular components
\vec V= V_x \hat x + V_y \hat y + V_z \hat z
in terms of cylindrical polar components
\vec V=V_r \hat r + V_\phi \hat \phi + V_z \hat z.

 

[od7]

I am trying to understand the tensor transformation law by applying it directly to a concrete example. If \vec V=V_x \hat x + V_y \hat \y + V_z \hat z then what do I end up with once I have applied the law?

 

[da615]

Could you show the tensor transformation law you are using and the details of your calculation?

 

[jcsd]

I'm not clear what it is exactly you're trying to do.

If you start out with a vector with compoents in caretsian cooridnates of (x,y,z) the coponents in cylindrical coordinates are (√(x^2 + y^2),arctan(y/x),z)