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Transforming from cartesian to cylindrical and spherical

  1. Sep 13, 2015 #1
    1. The problem statement, all variables and given/known data
    Translate the following equations from the given coordinate system into equations in each of the other two systems. Also, identify the surfaces so described by providing appropriate sketches.

    2. Relevant equations


    3. The attempt at a solution
    For my solutions, I obtained z=2r^2 for the cylindrical equation and for the spherical equation I got:
    (ρcosφ)^2 = 2(ρsinφcosθ)^2 + 2(ρsinφsinθ)^2. For my sketch I drew an infinite cylinder:
    DoubleCone.png
    I was wondering whether my conversions were correct, as when I transform the same equation from cartesian to spherical and from cylindrical to spherical I seem to obtain different equations.
     
  2. jcsd
  3. Sep 13, 2015 #2

    Mark44

    Staff: Mentor

    That's not a cylinder -- it's a cone. (Mathematically, cones have two parts.)

    What was your equation in Cartesian form?
     
  4. Sep 13, 2015 #3
    Sorry I meant cone hahah. My original equation in cartesian form was z^2=2x^2+2y^2
     
  5. Sep 13, 2015 #4

    Mark44

    Staff: Mentor

    Then your cylindrical equation should be ##z^2 = 2r^2##, not ##z = 2r^2## as you showed earlier.
     
  6. Sep 13, 2015 #5
    Does the spherical equation look correct?
     
  7. Sep 13, 2015 #6

    Mark44

    Staff: Mentor

    I'll take a look at it in a little while (it's dinner time...)
     
  8. Sep 13, 2015 #7
    Much appreciated (:
     
  9. Sep 13, 2015 #8

    Mark44

    Staff: Mentor

    This is correct, as far as you went, but the right side could be simplified considerably.
     
  10. Sep 13, 2015 #9
    How would you go about simplifying it?
     
  11. Sep 13, 2015 #10

    Mark44

    Staff: Mentor

    Expand the terms on the right side.
     
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