# Coordinate transformations

#### 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?

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#### mathwonk

Homework Helper
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

Homework Helper
Gold Member
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

Gold Member
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 (&radic;(x^2 + y^2),arctan(y/x),z)

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