I have no idea how to do this. I've tried alot of things but I can never reduce it to solely cartesian coordinates. Is there any hard fast procedure to conversions like this? thanks.
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Yes I have these. Except where ever yours have rho, I have r. That's ok. So can I just say that (rx), or (px) with your equations, is equal to [tex]x\sqrt{x^2+ y^2+ z^2}[/tex]
Let's say your vector in spherical coordinates is:
[tex] \vec S = (S_R, S_\theta, S_\phi) [/tex]
and cartesian,
[tex] \vec C = (C_x, C_y, C_z) [/itex]
Now if you want the x-component of [itex] \vec C [/itex] you use the dot product, [itex] \vec C \cdot \hat x [/itex], where [itex] \hat x = (1,0,0) [/itex] (in cartesian coordinates).
Now if you want the x-component of [itex] \vec S [/itex] you use the dot product, [itex] \vec S \cdot \hat x [/itex].
You need to express the unit vectors in the different coordinate system though. You can do this with geometry.
That makes it a little bit more difficult for you.