Solving a Restricted 3 Body Problem with Mathematica - Finding Velocity at Final Location

[Dustinsfl]

I used mathematica to solve a restricted 3 body problem and was able to export my position data at different time intervals. How can I find my velocity at that final location?

 

[Ackbach]

What mechanism did you employ in Mathematica to get your position object? NDSolve? If so, you should be able to differentiate it numerically by using the usual D[] function.

 

[Dustinsfl]

What mechanism did you employ in Mathematica to get your position object? NDSolve? If so, you should be able to differentiate it numerically by using the usual D[] function.

I obtained my position data by

XYdata = Flatten[
   Table[Evaluate[{x1[t], x2[t], x3[t]} /. s], {t, 0, 122400, 3}], 1];
SetDirectory[NotebookDirectory[]];
Export["OrbitData.txt", XYdata, "CSV"];
Earth = {N[x1], 0};
L4 = {N[xL4], N[yL4]};
Export["Earth.txt", Earth, "CSV"];

 

[Ackbach]

So are you now looking at the data in Excel, or Mathematica? Because you should be able to do x1'[t]/.s to get the derivative in Mathematica. In Excel, you'd have to have the time data as well as the position data. Then you could compute a numerical derivative.

 

[Dustinsfl]

Here is the plot of my trajectory to L4.
The moon is the green dot in the bottom and Earth is blue.