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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