Hello,

I am trying to model the flutter in a wing and have two coupled equations of motion. There are two parameters I am modeling, h and alpha. Equation 1 is a function of h, h', h'', alpha' and alpha''. The second is a function of alpha'', h'', alpha', and a. Through linearization I can reduce such a system to something of the form x' = f(x) where x' is a 4×1 matrix and f(x) is also a 4×1. I am attempting to solve such a condition with given values of h, alpha, h' and alpha', but I am unsure how to input these into ode45 properly. The full code I currently have is as follows.

`% Given parameters`

syms h a h_dot a_dotm = 1;x_m = 0.05;e = 0.4;zeta = 0.1;w_h = 0.5;w_a = 1.0;I_a = 0.25;D_a = 0.2;%GUESS U

U = 5;%

L = D_a*U^2*(a+h_dot/U);M = [1 x_m; (m*x_m)/I_a 1];C = [2*zeta*w_h 0; 0 2*zeta*w_a];K = [w_h^2 0; 0 w_a^2];G1 = [-L/m; (L*e)/I_a];G2 = [0;0];I = [1 0; 0 1];Z = [0 0; 0 0];A = [0.5*C M; I Z];B = [K 0.5*C; Z -I];F = [G1; G2];y = [h; a];y_dot = [h_dot; a_dot];x_vector = [y; y_dot];Ainv = inv(A);%RHS = -Ainv*B*x + Ainv*F;

% Initial Conditions

h = 0;a = 0;h_dot = 0;a_dot = 0;time = [0 5];fun = @(time,x) [x(2); -Ainv*B*x(1) + Ainv*F];[T,X] = ode45(fun, time, x_vector);plot(T, X(:,1));hold on plot(T, X(:,2));hold off

I provide this to answer any questions about variables or other names. However, the important section is below

`%RHS = -Ainv*B*x + Ainv*F;% Initial Conditionsh = 0;a = 0;h_dot = 0;a_dot = 0;time = [0 5];fun = @(time,x) [x(2); -Ainv*B*x(1) + Ainv*F];[T,X] = ode45(fun, time, x_vector);plot(T, X(:,1));hold on plot(T, X(:,2));hold off`

I get quite a few errors and unsure how to resolve them, any adivce is appreciated, thank you.

## Best Answer