Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Parametric Surfaces

  1. Apr 30, 2006 #1
    I need to take a surface integral where S is
    x^2 + y^2 + 2z^2 = 10. I need help with the parametrization of the curve. Letting x=u and y=v makes the problem too complicated. Can you let x=cos(u), y=sin(u) and z=3/sqrt(2)?
  2. jcsd
  3. Apr 30, 2006 #2


    User Avatar
    Science Advisor

    If z = 3/sqrt(2), then z is a fixed number. You only have one argument, u. So that's going to give you a curve with a fixed z-coordinate when you want a surface.

    You know you have an ellipsoid. One way to do this is to transform the ellipsoid into a sphere (a linear transformation--think geometrically), then use the spherical coordinates transformation. So your total transformation could be the composition of the transformation from spherical coordinates and the transformation from a sphere.
  4. Apr 30, 2006 #3


    User Avatar
    Science Advisor

    No, you can't for the very obvious reason that z is not a constant! It also has only one parameter where a surface integral requires 2. You can set [itex]x= \sqrt{10}cos(u)sin(v)[/itex], [itex]y= \sqrt{10}sin(u)sin(v)[/itex] and then put that into the equation: x2+ y2+ 2z2= 10sin2+ 2z2= 10. Hmm, suppose we let 2z2= 10cos2v? In other words, [itex]z= \sqrt{5}cos v][/itex] Then the equation reduces to
    10= 10 which is true. That is, those are parametric equations for the surface. Do you see how this uses spherical coordinates and varies it appropriately?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook