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

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Nikolas Haimerl 2019-10-7

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https://ww2.mathworks.cn/matlabcentral/answers/483941-how-can-i-solve-a-second-order-ode-backwards-in-simulink-or-matlab

评论： Nikolas Haimerl 2019-10-9

采纳的回答： Stephan

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