How can I solve a second order ODE backwards in simulink or matlab?

Hi,

I have a second order ODE of the form:

spp=inv(DD)*(tau-CC*[spx;spy;ap]-gg);

sppx=spp(1);

sppy=spp(2);

app=0;

Let q=(sx,sy,a), qp=(spx,spy,ap) and qpp=(sppx,sppy,app). Where qp=d/dt*q and qpp=d/dt*qp.

DD and CC are matrizes, tau and gg are vectors. These matrizes and vectors may contain variables of the vector q or qp.

I know how to solve this equation in simulink numerically for a specific initial condition at time t=0. However. I would like to know the solution of the ODE if I gave matlab not an initial condition but a solution at a certain point in time t1 != 0.

Specifically, the ODE above describes an object falling through the air and I would like to know the initial conditions q0 at time t=0 if I knew when the object hits the ground. So i know that at time t1 sy=0 and sx is some value sE.

Which method do I use for this kind of problem? I am grateful for any help.

Thanks

Answer 1

[Stephan]

It is allowed to integrate backwards with ode45 just by declaring tspan backwards:

tspan = [t1 0]

Then your ending conditions are used as initial conditions - you can do this without any special functions.

[Nikolas Haimerl]

THanks that was very helpful