Mathematica Asked on March 15, 2021
I need to export to a txt file the data from the following system of equations:
x'[t] == px[t],
y'[t] == py[t],
px'[t] == x[t]/(2*Sqrt[x[t]^2 + (1 - y[t])^2]),
py'[t] == -0.2 - (1 - y[t])/Sqrt[x[t]^2 + (1 - y[t])^2]
They can be reduced to two equations of x” and y”, but the number of initial conditions is the same so that’s arbitrary.
I successfully solved the system, for example, this way:
sol = NDSolve[{x''[t] == x[t]/(2*Sqrt[x[t]^2 + (1 - y[t])^2]),
y''[t] == -0.2 - (1 - y[t])/Sqrt[x[t]^2 + (1 - y[t])^2],
x[0] == x'[0] == Pi/3, y[0] == y'[0] == 0.5}, {x, y}, {t, -10,
1000}]
Now, how can I export the data from NDSolve
when y[t]==0
AND py[t]>0
? (in a 2-columm table txt file would be great)
Even if there is some kind of mistake (typo) the solution is to use WhenEvent
with Sow
and Reap
:
{sol, {pts}} =
Reap@NDSolve[{x''[t] == x[t]/(2*Sqrt[x[t]^2 + (1 - y[t])^2]),
y''[t] == -0.2 - (1 - y[t])/Sqrt[x[t]^2 + (1 - y[t])^2],
x[0] == x'[0] == Pi/3, y[0] == y'[0] == 0.5,
WhenEvent[y[t] == 0 && y'[t] > 0, Sow[{t, x[t]}]]}, {x, y}, {t, -10, 1000}];
which gives
pts
(* {{-0.655304, 0.444787}} *)
ready to export.
Correct answer by mmal on March 15, 2021
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