"Inverse of C matrix is Inf when it shouldn't be"
What do you expect the inverse of a non-invertible matrix to be?
"When I look at the C matrix the numbers do no look unusual enough to cause the inverse to be INF."
When I look at the C matrix all of the rows are copies of each other, which means that all of the rows are linearly dependent, which of course means that the matrix has no inverse, i.e. is not invertible.
Perhaps you looked at another matrix C.
So far neither INV nor MATLAB seem to be doing anything unexpected.
N=10;
V_inf = 50;
lambda = .5; %linspace(0,1,N)
S = 39.2699;
AR = 10.1859;
AoA = 8; % Angle of Attack in degrees
b = 20;
alpha_0 = 0; % Zero lift angle of attack is 0 due to airfoil being symmetric
cr = (2*b)/(AR*(lambda+1));
ct = cr*lambda;
i = 1;
alpha = AoA * (pi/180);
alpha_0 = alpha_0 * ones(N,1);
for theta = 0.01 % linspace(.01,pi-.01,20);
y = (b/2)*cos(theta);
if theta <= pi/2
c = (2/b)*cr*(1-lambda)*y+cr;
else
c = -(2/b)*cr*(1-lambda)*abs(y)+cr;
end
if length(alpha) == 1
alpha = alpha * ones(N,1);
end
if length(c) == 1
c = c * ones(N,1);
end
display(c)
C = zeros(N,N);
B = zeros(N,1);
for j = 1:N
for n = 1:N
C(j,n) = 2*b/(pi*c(j)) * sin(n*theta) + n * sin(n*theta)/sin(theta);
end
B(j,1) = alpha(j,1) - alpha_0(j,1);
end
display(C)
display(inv(C))
A = inv(C)*B
...
end
"The formula to calculate C is correct"
And yet clearly it isn't. Rather than relying on just believing that your code is correct, now is a good time to actually learn to look at what your code is really doing, not just what you imagine/hope/want/believe it to be doing. Actually looking at what code is really doing is an important step in debugging your code.
For example, your code defines c to be a column vector of one repeated value:
if length(c) == 1
c = c * ones(N,1);
end
and there is nothing else that depends on the loop iterator j when you calculate C, so clearly every row of C will also be exactly the same, based on that repeated value in c.
Note: of course it won't fix C's linearly dependent rows (and hence being non-invertible), but rather than using INV and MTIMES you should use the more robust MLDIVIDE operator:
A = C\B
See the "Tips" section here: https://www.mathworks.com/help/matlab/ref/mldivide.html#bthh_f9
