Help with solving a system of equations

Hi all,

For my aerodynamics class, I'm trying to solve a system of equations and get a result of something like this:

A1 = 0.239*alpha

A3 = 0.028*alpha

A5 = 0.0038*alpha

and so on up until A19 (the trend continues in odd numbers, i.e. A7, A9, A11, etc.)

The equation I start off with is with different theta values ranging from pi/6, pi/3, up til pi/2. But for some reason i am not getting values for A1, A3, A5, etc. Im quite a novice with MATLAB so im sure there's something im missing but please let me know cause I really need help with this one, and thanks in advance!

%% Case 1: N = 19

clc

clear

AR = 6;

b = 6;

Vinf = 1;

c = 1;

N = 19;

n = 1:2:N;

deltay = b./(N+1);

y0n = -(b./2)+n.*deltay;

theta = acos(-2*y0n/b);

syms alpha A(n)

S1 = symsum(A(n).*sin(n.*(theta)),n,1,N);

S2 = symsum(n.*A(n).*(sin(n.*(theta))./sin((theta))),n,1,N);

eq1 = (2*AR/pi)*S1+S2 == alpha;

[A,b] = equationsToMatrix(eq1, A(n));

x = linsolve (A,b)

Answer 1

[Stephan]

Please check carefully if this is correct and if it is what you need:

%% Case 1: N = 19
% clc
% clear

% b = 6;
% Vinf = 1;
% c = 1;

% deltay = b./(N+1);
% y0n = -(b./2)+n.*deltay;

N = 19;
AR = 6;
n =1:2:N;

syms alpha
A = sym('A', [1, N]);
A = A(1:2:end)

A = 

Pi = sym(pi)

Pi = 

π

theta = (linspace((Pi/6),(Pi/2),numel(n)).');

S1 = sum(A.*sin(n.*(theta)));
S2 = sum(n.*A.*(sin(n.*(theta))./sin((theta))));
eq1 = (2*AR/pi)*S1+S2 == alpha;
 
[A,b] = equationsToMatrix(eq1, A);
x = linsolve (A,b)

x = 

x_num = vpa(x)

x_num =