MATLAB: Second derivative of solution from ode45

Question

I have a system of 2 second order ODEs, which i converted to a system of fist order ODEs, which ode45 (or ode15s) needs as an input

my system input looks like this:

as an output i get the vector , but I need the derivatives and . How can i get those?

I tried using the gradient function as suggested by Star Strider in this question: How to output derivative from ODE 45 but unfortunately that did not help.

Thanks in advance!

Answer 1

After integrating your ODE-system you will have for some , and you have the function for your ODE-equations, f(t,X), one way to calculate the accelerations at times will be to simply call:

dxd2xdyd2ydt(i,:) = f(t_i,X(i,:));

Typically I use a regularly space array for the time in the call to ode45 and use the gradient-function, but the above should work - that is after all what we expect odeNN: to give us a solution X where that is true...

HTH