Coordinate transformations Spherical to Cartesian


by gaganaut
Tags: coordinate transfom, matrix, solids, spherical
gaganaut
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#1
Jan6-09, 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
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CompuChip
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#2
Jan6-09, 09:55 AM
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What do you mean, you don't know where it ends?
Isn't the (r, theta, phi) system relative to (x, y, z)?
gaganaut
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#3
Jan6-09, 10:03 AM
P: 20
Quote Quote by CompuChip View Post
What do you mean, you don't know where it ends?
Isn't the (r, theta, phi) system relative to (x, y, z)?
May be I am missing something very simple here. But I do not know the [tex](r,~\theta,~\phi)[/tex] as well. I did try to do it that way though to start with.

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.

CompuChip
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#4
Jan6-09, 01:05 PM
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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.
gaganaut
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#5
Jan6-09, 04:39 PM
P: 20
Quote Quote by CompuChip View Post
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.
Thanks Compuchip. I got your point. So stupid of me. The (x,y,z) can be used to find theta, phi. My bad.
CompuChip
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#6
Jan7-09, 03:21 AM
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You're welcome. We all get confused sometimes.


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