MATLAB Answers

Help with solving a system of equations

2 views (last 30 days)
Garrett
Garrett on 20 May 2021
Answered: Stephan on 20 May 2021
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)

Accepted Answer

Stephan
Stephan on 20 May 2021
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 = 

More Answers (0)

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!