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Math Help - Profile Curve

  1. #1
    Newbie
    Joined
    Feb 2011
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    11

    Unhappy Profile Curve

    This is translated from my own language, so feel free to correct me if I'm using a wrong translation.

    A profile curve in (x, z)-plan is given by the graph of the function z = ln (x), where
    x \epsilon [1, 2]. The profile curve is rotated the angle Pi around z-axis counterclockwise as seen from the z-axis'
    positive end. This yields the rotation surface F.

    Find a parametrization for the profile curve and F.
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  2. #2
    Senior Member
    Joined
    Mar 2010
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    <br />
F=ln(\sqrt{x^2+y^2})<br />

    In cylindrical coordinates

    <br />
F=ln \ r \ .<br />
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  3. #3
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    Feb 2011
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    Still need to find r(u,v) any help here?
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  4. #4
    Senior Member
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    Mar 2010
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    If this helps:

    <br />
u=x<br />

    <br />
v=y<br />


    <br />
F=ln \sqrt{u^2+v^2}<br />

    where

    <br />
v>=0 \ and \ 1<=\sqrt{u^2+v^2}<=2 \ .<br />
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  5. #5
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    Feb 2011
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    I think I'm being misunderstood.
    I need to find the parametrization/parametric equation for the profile curve and F.

    I was given this general equation:
    r(u,v)=(x(u,v),y(u,v)
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