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Position in Spherical Coordinates

  • Thread starter funcosed
  • Start date
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1. Homework Statement
This is a bit hard to describe without a decent picture (or a decent brain) but try to bare with me.
Picture below shows two spheres, if the origin is at centre of A, and a line d joins the centre of the two spheres, how do I describe the position of a point r from each sphere in spherical coordinates?

------------------r---------
A
------O---------------------
-----------------------------
-------------------O--------
B

2. Homework Equations
Polar coordinates are in terms of r and Ø
The point r described from the origin (at A) is given by (rAA), where r is line from origin to point r.

3. The Attempt at a Solution
If origin was at B it would have coordinates (rBB) need to write these in terms of rA and ØA.
I think rB=rA+d and Ø=ØBA
 

Answers and Replies

tiny-tim
Science Advisor
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hi funcosed! :smile:

why are you doing this? is it part of something else? :confused:

easiest would be to define Ø = 0 through B :wink:

(and perhaps to take the origin at the midpoint of AB instead of at A, or at the centre of mass)
 
37
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Re: Coordinates

For why I am doing it see here http://www.physforum.com/index.php?showtopic=28996"

Fairly sure I know what to do for most of the question but it doesn't seem to work out because the expression I get for part 3 is a mess which I think is because of the coordinates.
 
Last edited by a moderator:
tiny-tim
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ah i see … there's a vertical and horizontal direction that have to be regarded as fixed
Fairly sure I know what to do for most of the question but it doesn't seem to work out because the expression I get for part 3 is a mess which I think is because of the coordinates.
the cosine and sine rules should do it …

perhaps you'd better show your work (and a diagram), so that we can see why it's a mess? :smile:

(of course, a mess might be the right answer! :wink:)
 
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37
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Re: Coordinates

Part.3
ψA(r,Θ) = (1/4)Ua2(3r/a - a/r)sin2Θ

ψ(r,Θ)B = (1/4)Ua2((3r+d)/a - a/r)sin2Θ

Using, ψ(r,Θ) = ψA + ψ(r,Θ)B
and U = Ur + UΘ
Ur = (1/r2sinΘ)∂ψ/∂Θ
UΘ = (-1/rsinΘ)∂ψ/∂r

I get,
U = 1/2(UcosΘ)(3a/r - a3/r3 + 3a/4r2)r - 1/4(UsinΘ)(3a/r + a3/r3 + 3a/4r)Θ

which doesn't really fit with the form given in the question i.e. there are no a/d terms.
 
37
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Re: Coordinates

and heres a link to a picture

http://www.picpanda.com/viewer.php?file=lxvhtadg5vbj1miuycda.png" [Broken]
 
Last edited by a moderator:
tiny-tim
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sorry, i'm not following your equations at all :confused:
 

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