Position in Spherical Coordinates

In summary, the position of a point r from each sphere in spherical coordinates is described by (rA,ØA), (rB,ØB), and (Ur,UΘ).
  • #1
funcosed
37
0

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

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.

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
 
Physics news on Phys.org
  • #2
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)
 
  • #3


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:
  • #4
funcosed said:

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:)
 
Last edited by a moderator:
  • #5


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.
 
  • #6


and here's a link to a picture

http://www.picpanda.com/viewer.php?file=lxvhtadg5vbj1miuycda.png" [Broken]
 
Last edited by a moderator:
  • #7
sorry, I'm not following your equations at all :confused:
 

1. What are spherical coordinates?

Spherical coordinates are a system of describing the position of a point in three-dimensional space using the distance from the origin, an angle from the positive z-axis, and an angle from the positive x-axis.

2. How do spherical coordinates differ from Cartesian coordinates?

Spherical coordinates use angles and distances from the origin, while Cartesian coordinates use distances along three perpendicular axes (x, y, and z).

3. What is the range of values for each component in spherical coordinates?

The distance from the origin (r) can range from 0 to infinity, the angle from the positive z-axis (θ) can range from 0 to π (180 degrees), and the angle from the positive x-axis (φ) can range from 0 to 2π (360 degrees).

4. How are spherical coordinates converted to Cartesian coordinates?

To convert from spherical to Cartesian coordinates, the following equations can be used:
x = r * sinθ * cosφ
y = r * sinθ * sinφ
z = r * cosθ

5. In what fields of science are spherical coordinates commonly used?

Spherical coordinates are commonly used in fields such as astronomy, physics, and geology, where spherical objects or systems are studied, and in engineering, where they are used in 3D modeling and design.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
285
  • Introductory Physics Homework Help
Replies
7
Views
260
  • Introductory Physics Homework Help
Replies
18
Views
3K
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
21
Views
587
  • Introductory Physics Homework Help
Replies
1
Views
769
  • Introductory Physics Homework Help
Replies
3
Views
3K
Replies
2
Views
981
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
780
Back
Top