# Solving a complex system of differential equations

7 vues (au cours des 30 derniers jours)
Ali Almakhmari le 15 Nov 2023
Commenté : Torsten le 15 Nov 2023
I have a this differential equation system: , where F is a function of time (t). But I am not sure whats the easiest way to solve it in MATLAB. Lets say for example:
M = [1,0.8;0.8,7]
K = [5,0;0,10]
D = [0.15,0;0,0.35]
F = [5*exp(i*5*t); 3.65*exp(i*5*t)]
q = [X; Y]
And we want to solve for q, which is X and Y.
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### Réponse acceptée

Torsten le 15 Nov 2023
Modifié(e) : Torsten le 15 Nov 2023
%q(1) = X, q(2) = Y, q(3) = Xdot, q(4) = Ydot
M = [1,0.8;0.8,7];
K = [5,0;0,10];
D = [0.15,0;0,0.35];
F = @(t)[5*exp(i*5*t); 3.65*exp(i*5*t)] ;
tspan = [0 1];
q0 = [0 1 1 0].';
fun = @(t,q)[[q(3);q(4)];inv(M)*(F(t)-(1i*D+K)*[q(1);q(2)])];
[T,Q] = ode45(fun,tspan,q0);
figure(1)
hold on
plot(T,real(Q(:,1)))
plot(T,imag(Q(:,1)))
hold off
figure(2)
hold on
plot(T,real(Q(:,2)))
plot(T,imag(Q(:,2)))
hold off
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Ali Almakhmari le 15 Nov 2023
Is the first plot for q(1) and q(2) or is it for q(3) and q(4)? Because the definition of fun makes me think its q(3) and q(4)
Torsten le 15 Nov 2023
The first plot is for the real and imaginary part of q(1) = X, the second plot is for the real and imaginary part of q(2) = Y.
q(3) and q(4) are Xdot and Ydot, respectively (as written in the headline of the code).

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