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Math Help - Principal Curvature

  1. #1
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    Dec 2009
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    Principal Curvature

    Hi,

    I am trying to understand a theoretical problem involving the contact between two surfaces. I have uploaded a screen shot of the mathematical formulations of the solution.

    I understand most of the solution, except the principal curvatures. I have tried to look up principal curvature, but still not sure how is applied to this problem.

    I would really appreciate any help for the mathematicians out there.

    https://dl.dropbox.com/u/47274064/Prin_curve_1.JPG

    Thanks.
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  2. #2
    Senior Member
    Joined
    May 2010
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    Los Angeles, California
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    Re: Principal Curvature

    Principal curvatures are defined as follows: take a plane through the point that contains the normal and interesct it with the surface to get a curve. As you rotate the plane around you get different curves of varying curvature and the maximum and minimum values of this normal curvature are the principal curvatures. Take a look at Do Carmo's book entitled Differential Geometry of Curves and Surfaces. It's one of the best texts on this topic.
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