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Math Help - Mean curvature of a surface

  1. #1
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    Mean curvature of a surface

    Hi everyone, new here and trying to calculate the mean curvature for the following surface:

    r(u,v)=ui+f(u)cos(v)j+f(u)sin(v)k


    I have been through the process of finding tangent vectors and a unit normal vector to the surface, so up to the point where I have had to substitute 6 scalars into:

    h(p)=
    aG-2bF-cE
    2(EG-F2)

    The only problem I seem to be having is not being able to simplify it... This is what I have:

    h(p)=
    f''(u)f(u)2-f'(u)2-1
    2f(u)(1+f'(u)2)√(cos2(2v)f'(u)+1)

    Maybe missing something really simple here or I have made a mistake in calculating the scalars.

    Any help, much appreciated!
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  2. #2
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    Re: Mean curvature of a surface

    Mean curvature of a surface-task1equation.jpg

    I have worked through this again and shamefully the original post had some errors in. I have attached a correct answer, however still stuck with having to derive the differential equation!
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  3. #3
    Member
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    Mar 2013
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    BC, Canada
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    Re: Mean curvature of a surface

    From this link, because it would be a lot of typesetting:

    Mean curvature of a surface-7bc2c770196ecff8e74661460ac33367.png

    Replace S(x,y) with your r(u,v). Respond with calculated partial derivatives as in the formula so we can see where you are going wrong.
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