Coordinate transformations Spherical to Cartesianby gaganaut Tags: coordinate transfom, matrix, solids, spherical 

#1
Jan609, 09:50 AM

P: 20

Hi,
I would like to transform a vector from Spherical to cartesian coordinate system. But the question is probably not that straight forward. :( I have a vector say [tex]E = E_r~\hat{r}+E_{\theta}~\hat{\theta}+E_{\phi}~\hat{\phi}[/tex]. But I know only the cartesian coordinate from where it starts, say [tex](x,y,z)[/tex] and I do not know where it ends. So I am unable to find angles [tex]\theta[/tex] and [tex]\phi[/tex] for computing the transformation matrix [tex]R[/tex] that transforms the vector [tex]E[/tex] to cartesian system. This [tex]R[/tex] is the usual matrix with sines and cosines of [tex]\theta[/tex] and [tex]\phi[/tex] and can be seen here. http://en.wikipedia.org/wiki/Vector_...al_coordinates So how do I go about it. Is there even a way to do this. Once again this is not a homework question and is for a small project that I am doing. There aren't any homeworks at this time of the year. :) Appreciate any form of help. Kedar 



#2
Jan609, 09:55 AM

Sci Advisor
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P: 4,301

What do you mean, you don't know where it ends?
Isn't the (r, theta, phi) system relative to (x, y, z)? 



#3
Jan609, 10:03 AM

P: 20

All I know is the magnitudes in the [tex]\hat{r},~\hat{\theta}[/tex] and [tex]\hat{\phi}[/tex] directions and the starting point. And nothing else. Can the [tex](r,~\theta,~\phi)[/tex] be found out from the magnitudes in the [tex]\hat{r},~\hat{\theta}[/tex] and [tex]\hat{\phi}[/tex] ([tex]E_r,~E_{\theta},~E_{\phi}[/tex] as above)? It can be really simple. But I cannot just think about it right. 



#4
Jan609, 01:05 PM

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P: 4,301

Coordinate transformations Spherical to Cartesian
Yes, you might be missing something or I might.
But aren't the coordinate values simply the coefficients of the unit vectors? Like, in a Cartesian system you can write either (3, 0, 2) for the coordinates of a point, or you can describe it by a vector [itex]3 \hat x + 0 \hat y  2 \hat z[/itex]. When writing down a tuplet of numbers like (3, 0, 2), we are implicitly assuming that we have these three basis vectors [itex]\hat x, \hat y, \hat z[/itex] and we are using them to fix our point. 



#5
Jan609, 04:39 PM

P: 20





#6
Jan709, 03:21 AM

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P: 4,301

You're welcome. We all get confused sometimes.



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