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Thread: 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 $\displaystyle \epsilon$ [1, 2]. The profile curve is rotated the angle $\displaystyle Pi$ 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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    $\displaystyle
    F=ln(\sqrt{x^2+y^2})
    $

    In cylindrical coordinates

    $\displaystyle
    F=ln \ r \ .
    $
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  3. #3
    Newbie
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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:

    $\displaystyle
    u=x
    $

    $\displaystyle
    v=y
    $


    $\displaystyle
    F=ln \sqrt{u^2+v^2}
    $

    where

    $\displaystyle
    v>=0 \ and \ 1<=\sqrt{u^2+v^2}<=2 \ .
    $
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  5. #5
    Newbie
    Joined
    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:
    $\displaystyle r(u,v)=(x(u,v),y(u,v)$
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