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Homework Help: Parabolic coordinate system question

  1. Sep 14, 2008 #1
    1. The problem statement, all variables and given/known data

    a 3D solid is bounded by 2 paraboloids. The binding condition in cartesian coordinates is

    -1+(x2+y2) < 2z < 1-(x2+y2)

    a) rewrite the binding condition in parabolic coordinates
    b) using parabolic coordinates and the (already derived) metric tensor, find the volume of the solid

    2. Relevant equations

    x=stcos(p) y= stsin(p) z= (t2-s2)/2

    3. The attempt at a solution

    I found the binding conditions to be equal to

    -1 + s2t2 < t2 - s2 < 1 - s2t2

    I have the metric tensor and I know i just need to do a triple integral and multiply by the square root of the metric tensor but how do I find the functions of s, t and p and how do I know the limits of integration?

    I've tried splitting it into two inequalities and moving the variables around looking for a pattern but I can't really see anything.

    any help would be greatly appreciated

    thank you

    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Sep 15, 2008 #2
    Never mind
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