Second derivative of solution from ode45
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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?
, 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!
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Bjorn Gustavsson
2020-11-4
编辑：Bjorn Gustavsson
2020-11-4
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:
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
8 个评论
James Tursa
2020-11-4
You have expressions for ODE1 and ODE2. Simply plug the solution from ode45 into those expressions to get your 2nd derivative values.
Bjorn Gustavsson
2020-11-4
@e_frog: Do you wonder how to write your ODE-function?
If so, let's make a 1-D harmonic oscillating ODE, i.e.
That would become a function something like this:
function dxdtd2xdt2 = ode_ex_ho(t,x,k)
dxdtd2xdt2 = [x(2);
-k*x(1)];
end
Such a function you can adjust as you need.
HTH
@Bjorn
Thats exactly how I converted my second order ODEs to a first order system. I would call the example function like this:
[t,X] = ode45(@(t,X) ode_exo_ho(t,X,k),tspan,y0)
The Problem with that is, that the coutput vector X
would in this example be 
but I need 
(respectively for my case with 2 ODEs I would need 
and 
)
and )
James Tursa
2020-11-4
编辑：James Tursa
2020-11-4
Please show us the expressions for ODE1 and ODE2. I still don't understand why you are having trouble plugging x and xdot into these expressions to get xdotdot. Why can't you just call ode_exo_ho( ) with the appropriate inputs to get what you want?
e_frog
2020-11-4
James Tursa
2020-11-4
编辑：James Tursa
2020-11-4
If the ode_exo_ho( ) function is vectorized (meaning it will accept vectors and properly calculate a vector result), then yes it is just this easy. If ode_exo_ho( ) is not vectorized, then you would have to call it in a loop, but still pretty easy.
The ease of vectorizing your function depends on what it is doing. Sometimes it is just a simple matter of replacing the operators * and / and ^ with their element-wise counterparts .* and ./ and .^
e_frog
2020-11-5
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