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Spherical coordinates confusion

  1. Oct 21, 2014 #1
    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?
     
  2. jcsd
  3. Oct 21, 2014 #2

    jedishrfu

    Staff: Mentor

    Last edited: Oct 21, 2014
  4. Oct 21, 2014 #3
    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.
     
  5. Oct 28, 2014 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    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.
     
  6. Oct 28, 2014 #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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