Geometric interpretation of Legendre polynomials and orthogonal polynomials

[tardon007]

hi folks!

I have been trying to figure out some plausible geometric intrepretation to legendre polynomials and what are they meant to do.

I have come across the concept of orthogonal polynomials while working with some boundary value problems in solid mechanics and wasn't able to come to terms with that since then.

Can some one amongst you suggest a beginner's literature on this ?

It would be invalueble if someone can share ur insights on this ?

 

[BobG]

Try this link:

http://www.floridageomatics.com/publications/gfl/toc.htm

The section on Legendre polynomials, zonal harmonics, sectorial harmonics, and tesseral harmonics are in the appendix.

It's basically a sine regression. You have an actual shape of a non-perfect sphere that you want to model. Legendre polynomials give you a method of creating an equation that will model the irregularities in the object's shape.