Data from 2nd order ode mathematica

[Dustinsfl]

How can I extract time data from a system 2nd order ODEs in Mathematica?

 

[Ackbach]

Can you post the ODE's and your Mathematica code so far?

 

[Dustinsfl]

Can you post the ODE's and your Mathematica code so far?

Numerical Simulation of the 2-Body Problem

ClearAll["Global`*"];

We begin with of the the necessary data for this problem...

M = 5974*10^21; (* mass of Earth, kg *)

m = 1000; (* mass of  spacecraft , kg *)

\[Mu] = 3.986*10^5; (* gravitaional parameter, based on km units of length, \
km/s for velocity *)

Rearth = 6378; (* radius of the Earth, km *)Simulation Inputs

r0 = {3950.55, 43197.9, 0};(* initial position vector, km *)
v0 = {3.3809, -7.25046, 0}; (* initial velocity vector, km *)
Days = 1/10; (* elapsed time of simulation days *)

\[CapitalDelta]t = Days*24*3600;(* convert elapsed days to seconds *)

s = NDSolve[
   {
    x1''[t] == -(\[Mu]/(Sqrt[x1[t]^2 + x2[t]^2 + x3[t]^2])^3)*x1[t],
    x2''[t] ==  -(\[Mu]/(Sqrt[x1[t]^2 + x2[t]^2 + x3[t]^2])^3)*x2[t],
    x3''[t] ==  -(\[Mu]/(Sqrt[x1[t]^2 + x2[t]^2 + x3[t]^2])^3)*x3[t],
    
    x1[0] == r0[[1]], (* intial x-position of satellite *)
    
    x2[0] == r0[[2]],(* intial y-position of satellite *)
    
    x3[0] == r0[[3]],(* intial y-position of satellite *)
    
    x1'[0] == v0[[1]],(* intial vx-rel of satellite *)
    
    x2'[0] == v0[[2]],(* intial vy-rel of satellite *)
    
    x3'[0] == v0[[3]](* intial vy-rel of satellite *)
    
    },
   {x1, x2, x3},
   {t, 0, \[CapitalDelta]t} 
   ];

Plot of the Trajectory Relative to Earth

g1 = ParametricPlot3D[
   Evaluate[{x1[t], x2[t], x3[t]} /. s], {t, 0, \[CapitalDelta]t},  
   PlotStyle -> {Red, Thick}];
g2 = Graphics3D[{Blue, Opacity[0.6], Sphere[{0, 0, 0}, Rearth]}];Show[g2, g1, Boxed -> False]

 

[BillSimpson]

I'm not certain exactly what you are expecting when you "extract time data", but perhaps something in this will help.What if you replaceShow[g2, g1, Boxed -> False]

with

g3 = Graphics3D[Table[Point[{x1[t], x2[t], x3[t]} /. s[[1]]], {t, 0, Δt, Δt/10}]];
g4 = Graphics3D[Table[Text[ToString[t], {x1[t], x2[t], x3[t]} /. s[[1]], {1, 0}], {t, 0, Δt, Δt/10}]];
Show[g2, g1, g3, g4, Boxed -> False]That will place points along your path and label each point with the associated value of t. You can adjust the step size and the label position next to each point as needed.

If that doesn't provide you with the necessary level of detail then you might try using

Table[{t,x1[t],x2[t],x3[t]}/.s[[1]], {t,0,Δt,Δt/10}]//TableForm

with appropriate step size to give you the numerical results to go along with your plot.

 

[alphy]

To extract time data from a system of 2nd order ODEs in Mathematica, you can use the "NDSolve" function to solve the system and generate a numerical solution. This function allows you to specify the time range for which you want to solve the system, and then outputs the solution as a list of data points at different time intervals. You can then use the "Part" function to extract the time data from this list and use it for further analysis or plotting. Additionally, you can also use the "Table" function to generate a table of time and corresponding solution values, giving you more control over the time data extraction process.