Spherical coordinates confusion

  • Thread starter kkz23691
  • Start date
  • #1
47
5
I am accustomed to
##x=rcos(\theta)sin(\phi)##
##y=rsin(\theta)sin(\phi)##
##z=rcos(\phi)##
##-\pi<\theta<\pi##, ##-\pi/2 < \phi < \pi/2##

but see some people using these instead
##x=rcos(\theta)cos(\phi)##
##y=rsin(\theta)cos(\phi)##
##z=rsin(\phi)##
##-\pi<\theta<\pi##, ##-\pi/2 < \phi < \pi/2##

Have you seen this before?
The second set seems to be "oblate spheroidal coordinates" (http://en.wikipedia.org/wiki/Oblate_spheroidal_coordinates) in the limit where the oblate spheroid is actually a sphere (the argument of the hyperbolic sin/cos is large enough so that
##asinh(\mu)=acosh(\mu)=r=\mbox{const}##

Does this make sense?
 

Answers and Replies

  • #3
47
5
Thanks jedishrfu, I just checked one article that uses these and indeed, the ##\phi## angle is relative to the XY-pane! Also, some use
x=rcos(θ)cos(ϕ)
y=rsin(θ)cos(ϕ)
z=-rsin(ϕ)
−π<θ<π, −π/2<ϕ<π/2
which probably work fine, even though the "minus" sign in z doesn't match the definition of "oblate spheroidal coordinates" (because the hyperbolic functions are assumed positive there)

If
z=-rsin(ϕ)

doesn't seem right, please post.
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
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I have always seen [itex]\rho[/itex] rather than r but using [itex]\phi[/itex] to mean the angle a line from the origin to the point makes with the z-axis is a "mathematics" notation while using [itex]\theta[/itex] for that is a "physics" notation.
 
  • #5
47
5
Yes HallsofIvy certainly agree with you! What was new to me - measuring the inclination w/respect to xy-plane; I guess this is a "geography" notation :)
 

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