Problem with matrix differential equation resolve in Matlab with ode45

Hi,

I would like to solve this linearized matrix differential equation:

My program has no errors but the result it gives seems inconsistent. Here is my program:

vt= linspace(0,10,500);
v=0.5*vt;

Q0=[0 0;0 0];

tspan=[0 10];

M=[80.8 2.32;2.32 0.28];
K0=[-80.95 -2.6;-2.6 -0.8];
K2=[0 76.6 ; 0 2.65];
C1=[0 33.87; -0.86 1.68];

q=ones(2,2);

[tSol,QSol]=ode45(@(tSol,QSol) myodefun(tSol,q,vt,v,M,K0,K2,C1,f),tspan,Q0);

function dQdt=myodefun(t,q,vt,v,M,K0,K2,C1)
v=interp1(vt,v,t);
Q1=q(:,1);
Q2=q(:,2);
dQ1dt=M*Q2;
dQ2dt=-v*C1*Q2-(9.81*K0+v*v*K2)*Q1;
dQdt=[dQ1dt;dQ2dt];
end

Do you see anything I did wrong to solve this equation?

Answer 1

[James Tursa]

Normally I would have expected ode45( ) to pass q as a 4x1 column vector. Also, I don't see anything in your code solving for qdotdot that would involve backslash or the inverse of M. E.g., something like this for a derivative function:

% assume q is passed in as 4x1 column vector
function dQdt=myodefun(t,q,vt,v,M,K0,K2,C1)
v=interp1(vt,v,t);
qdot = q(3:4);
q = q(1:2);
qdotdot = M \ (-v*C1*qdot - (9.81*K0+v*v*K2)*q);
dQdt=[qdot;qdotdot];
end

And what is f? I don't see that defined. And I don't see it being used in myodefun.

[Antoine W]

Thanks for your answer, f is just a parameter I forgot to remove. By just adding a reshape on q and qdot, your program works. However when outputting to QSol in what orders is it returned between phidt deltadt phi and delta?

[James Tursa]

[phi,delta,phidot,deltadot]