Solve 2D Particle Motion: NDSolve with Non-Constant Deceleration in Mathematica

[Niles]

Hi

I am succesfully using NDSolve to find the solution of a 1D equation of motion:

solution = NDSolve[{x''[t] == -200, x[0] == 0, x'[0] == 100}, x, {t, 0, 1}];
ParametricPlot[{x[t], x'[t]} /. solution, {t, 0, 1}, PlotRange -> {{0, 100}, {0, 100}}]

This is a particle decelerating constantly in the x-direction. Now, I need to extend my problem, because the deceleration along x is actually not constant. It depends on both the x- and y-coordinate of the particle.

So the total problem is
$$\frac{d^2x}{dt^2} = -200y - x\\ \frac{dy}{dt} = -2$$
So along x there is non-constant deceleration, and along y I have a constant velocity. Is it possible to solve such a problem in Mathematica?

Best regards and thanks in advance,
Niles.

 

[phyzguy]

Sure:

solution = 
 NDSolve[{x''[t] == -200 y[t] - x[t], y'[t] == -2, x[0] == 0, 
   x'[0] == 100, y[0] == 0}, {x[t], y[t]}, {t, 0, 1}]

 

[Niles]

Thanks, that is kind of you. NDSolve is a pretty powerful tool.

The initial condition y'(0) is something that changes for different problems. However, my particle is not allowed to move further than y=5. If it does so, then it is "lost", and its solution is not relevant to my problem any longer. Is there a way to incorporate this into NDSolve, i.e. that it should stop calculating further if y(t) == 5?Niles.