How can I call the highest order solution (e.g. x'') of an ode in another ode?

Question

Leonie Schickmann 2021-2-24

0
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https://ww2.mathworks.cn/matlabcentral/answers/754714-how-can-i-call-the-highest-order-solution-e-g-x-of-an-ode-in-another-ode

评论： Leonie Schickmann 2021-2-24

I want to solve the following differential equations, a-f are known variables which are manually set before solving the equations:

u'' = -a/d*u' - b/d*u - x''

x''= (c+d)^(-1)*( - e*x' - f*x - d*u'')

I do not know how to call x'' in the first and u'' in the second ode. My approach (given below) does run, but the results are wrong (u and u' are always 0). How do I implement my equations correctly?

The code I tried to use:

tspan = [0 200];
z0    = [0; 0; 5; 0];
[t,z] = ode45(@(t,z)f(t,z),tspan, z0);
function dzdt = f(t,z)
u = z(1:2);
x = z(3:4);
% Definition of a-f here 
dzdt = zeros(4,1);              
dzdt(1) = u(2);
dzdt(2) = -a/d *u(2)-b/d *u(1)-dzdt(4);
dzdt(3) = x(2);
dzdt(4) = (c+d)^(-1)*(-e*x(2)-f*x(1)-d*dzdt(2));
end