- #1
paxprobellum
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Homework Statement
The problem is from a text on FEA, but I've "solved" the problem down to an eignenvalue/eigenvector problem. The point is to show that L_n = (2n-1)pi / (2a) and that the solution u(r,T) = sum [ a_n r^(L_n) ( cos (L_n * T) + (-1)^n sin (L_n * T) ] for n = 1 to infinity.
L = lambda, T = theta
Homework Equations
r^L (c1 cos(aL/2) + c2 sin(aL/2) ) = 0
L r^L (c1 sin(aL/2) + c2 cos(aL/2) ) = 0
The Attempt at a Solution
I want to get it into the form (A-LB)x = 0 to solve it using MATLAB (sptarn, e.g.) but I don't know how. So I moved on to say that if Ax = 0 and there are nontrivial solutions, than the determinant of A is zero as:
det( [cos(aL/2) sin(aL/2) ; sin(aL/2) cos(aL/2)] ) = 0
but that gives me aL/2 = 0 (cos^2 + sin^2 = 1), which is not the answer. So I'm a bit stuck.