# Principal Curvature

• Aug 14th 2012, 04:47 AM
OptiEng
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.
• Aug 15th 2012, 05:26 PM
ojones
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.