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Coto
#4
Jun10-10, 12:34 AM
P: 308
Boundary conditions, Sturm-Liouville, & Gauss Divergence

Quote Quote by the_dialogue View Post
Could it be that the author is saying that the boundary motion (f) is equal to 2 terms (in general): [1] using the small angle approx, the component of the membrane movement + [2] some multiple of the membrane movement (alpha)? This seems kind of weak.
Hmm. It's a tough one. I personally don't see how the alpha is coming in either. What's the name of the paper? Is it accessible through web of science?

Quote Quote by the_dialogue View Post
I'm not so sure what you mean. Where are these Sturm-Liouville equations taken from and how are they relevant to the problem? Perhaps a simpler example (somewhere online) would help explain this?
I would say don't get too caught up in where they are coming from. It is more important to understand why they are useful. My guess is the author is deriving a set of bases functions to be used in an expansion of [tex]u(x)[/tex]. The Sturm-Liouville equations can deliver a set of functions which can serve this purpose. The nice properties that these bases functions display make them a good choice when you're expanding the unknown u(x).

In particular take a look at (http://en.wikipedia.org/wiki/Asymptotic_expansion) and (http://en.wikipedia.org/wiki/Perturbation_methods).