Solving a complex system of differential equations
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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:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1540052/image.png)
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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Torsten
2023년 11월 15일
편집: Torsten
2023년 11월 15일
%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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Torsten
2023년 11월 15일
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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