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Spherical Coordinates

  1. Mar 8, 2009 #1
    The problem statement, all variables and given/known data
    The outermost integral is:
    -2 to 2, dx

    The middle integral is:
    -sqrt(4-x^2) to sqrt(4-x^2), dy

    The inner most integral is:
    x^+y^2 to 4, dz






    The attempt at a solution

    Drawing the dydx in a simple 2d (xy) plane, it is circular with a radius of 2. So this means that the period(theta) will go from 0 to 2pi. Drawing in 3d (xyz) yields a hemisphere/paraboloid. Now this is where I'm stuck. I don't know what to do after this or how to really tackle this problem. Do I want to attempt to draw a 'slice' of it in the spherical outline with the variables phi, rho, theta? Do I have to look at it a certain way (2d or 3d)? I just don't see what I can do!

    Any help or guidance is greatly appreciated!!
     
  2. jcsd
  3. Mar 8, 2009 #2

    gabbagabbahey

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    You haven't actually said what the question asks you to do..
     
  4. Mar 8, 2009 #3
    Whoops. Thought I stuck that in there. Anyways, all I have to do is convert it to spherical coordinates (from rectangular to spherical).
     
  5. Mar 8, 2009 #4

    gabbagabbahey

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    I was afraid of that :wink:

    It is indeed a paraboloid, so [itex]\rho[/itex] and [itex]\phi[/itex] will not be independent the way they would if it was a spherical section....

    Try finding the relationship between [itex]\rho[/itex] and [itex]\phi[/itex] for the paraboloid's curved and flat surfaces
     
  6. May 10, 2009 #5
    From my weblog
    http://buyanik.wordpress.com/2009/05/02/laplacian-in-spherical-coordinates/" [Broken]
     
    Last edited by a moderator: May 4, 2017
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