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Math Help - [SOLVED] Separable Laplacians

  1. #1
    Forum Admin topsquark's Avatar
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    [SOLVED] Separable Laplacians

    Here's my version of a double post. I asked this same question a couple of years ago, but we now have a bunch of new members, so I thought I'd give it another go.

    I read somewhere that Laplace's equation is separable in 11 different (presumably orthogonal) coordinate systems. Obviously there is Cartesian, cylindrical, and spherical-polar. Does anyone know of other coordinate systems? Thanks!

    -Dan
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by topsquark View Post
    Here's my version of a double post. I asked this same question a couple of years ago, but we now have a bunch of new members, so I thought I'd give it another go.

    I read somewhere that Laplace's equation is separable in 11 different (presumably orthogonal) coordinate systems. Obviously there is Cartesian, cylindrical, and spherical-polar. Does anyone know of other coordinate systems? Thanks!

    -Dan
    Conical, oblate spheroidal, prolate spheroidal, parabolic, parabolic cylindrical, paraboloidal, ellipsoidal.
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  3. #3
    Forum Admin topsquark's Avatar
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    Dang it all! How did you do that? I tried every variation on a search that I could think of and got nowhere. When I looked up conical coordinates the bottom of the Wikipedia page had the whole darned list.

    I stink at web searches. (sigh)

    Thanks for the info!

    -Dan
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by topsquark View Post
    Dang it all! How did you do that? I tried every variation on a search that I could think of and got nowhere. When I looked up conical coordinates the bottom of the Wikipedia page had the whole darned list.

    I stink at web searches. (sigh)

    Thanks for the info!

    -Dan
    Anytime Topsquark, I went to Wolfram MathWorld: The Web's Most Extensive Mathematics Resource and typed in Laplace's equation

    and got this

    Laplace's Equation -- from Wolfram MathWorld
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