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Homework Help: Convert ellipsoid from cartesian to spherical equation

  1. Jan 29, 2012 #1
    1. The problem statement, all variables and given/known data

    In order to advance on a problem I'm working, I need to covert this ellipsoid from cartesian to spherical coordinates.
    [tex] \frac{x^2}{a^2} +\frac{y^2}{b^2} +\frac{z^2}{c^2} = 1 [/tex]

    2. Relevant equations

    [tex] x^2 +y^2+z^2= \rho ^2 [/tex]
    [tex] x=\rho sin \phi cos \theta [/tex]
    [tex] y= \rho sin \phi sin \theta [/tex]
    [tex] z= \rho cos \phi [/tex]

    3. The attempt at a solution

    I'm not sure how to use those formulas because they look like they would only work with a sphere. I don't know. It's been a semester since calc three and we didn't do spherical coordinates anyway. What do I do?
  2. jcsd
  3. Jan 29, 2012 #2
    using what I foud here: http://math.wikia.com/wiki/Ellipsoid

    would I have
    [tex] x=asin\phi cos \theta [/tex]
    [tex] y=bsin \phi sin \theta [/tex]
    [tex] z= ccos\phi [/tex]

    Thus, [tex] \rho ^2= a^2 sin^2 \phi cos^2 \theta + b^2 sin^2 \phi sin ^2 \theta + c^2 cos ^2 \phi [/tex] ?
  4. Jan 30, 2012 #3

    I like Serena

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    Looks like you've solved it! :)
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