MHB Following on to ODE thread 2nd order to 1st

[Dustinsfl]

I am getting this error in Mathematica from the code below:
Computed derivatives do not have dimensionality consistent with the initial conditions

ClearAll["Global`*"]
\[Mu] = 398600;
s = NDSolve[{x1'[t] == x2[t],
    y1'[t] == y2[t],
    z1'[t] == z2[t], 
    x2'[t] == -\[Mu]*x1[t]/(x1[t]^2 + y1[t]^2 + z1[t]^2)^{3/2}, 
    y2'[t] == -\[Mu]*y1[t]/(x1[t]^2 + y1[t]^2 + z1[t]^2)^{3/2}, 
    z2'[t] == -\[Mu]*z1[t]/(x1[t]^2 + y1[t]^2 + z1[t]^2)^{3/2}, 
    x1[0] == -201000*Sqrt[3],
    y1[0] == 201000,
    z1[0] == 0,
    x2[0] == -2.04119,
    y2[0] == 0.898024,
    z2[0] == 0}, {x, y, z}, {t, 0, 50}];

 

[Ackbach]

I don't have MMA handy to use, but a few things I see you might change:

ClearAll["Global`*"]
\[Mu] = 398600;
s = NDSolve[{x1'[t] == x2[t],
    y1'[t] == y2[t],
    z1'[t] == z2[t], 
    x2'[t] == -\[Mu]*x1[t]/(x1[t]^2 + y1[t]^2 + z1[t]^2)^(3/2), 
    y2'[t] == -\[Mu]*y1[t]/(x1[t]^2 + y1[t]^2 + z1[t]^2)^(3/2), 
    z2'[t] == -\[Mu]*z1[t]/(x1[t]^2 + y1[t]^2 + z1[t]^2)^(3/2), 
    x1[0] == -201000*Sqrt[3],
    y1[0] == 201000,
    z1[0] == 0,
    x2[0] == -2.04119,
    y2[0] == 0.898024,
    z2[0] == 0}, {x1,x2, y1,y2, z1,z2}, {t, 0, 50}];

So I changed the curly braces to parentheses, as well as added the correct dependent variables in the list at the bottom. Does that work?

 

[Dustinsfl]

I don't have MMA handy to use, but a few things I see you might change:

ClearAll["Global`*"]
\[Mu] = 398600;
s = NDSolve[{x1'[t] == x2[t],
    y1'[t] == y2[t],
    z1'[t] == z2[t], 
    x2'[t] == -\[Mu]*x1[t]/(x1[t]^2 + y1[t]^2 + z1[t]^2)^(3/2), 
    y2'[t] == -\[Mu]*y1[t]/(x1[t]^2 + y1[t]^2 + z1[t]^2)^(3/2), 
    z2'[t] == -\[Mu]*z1[t]/(x1[t]^2 + y1[t]^2 + z1[t]^2)^(3/2), 
    x1[0] == -201000*Sqrt[3],
    y1[0] == 201000,
    z1[0] == 0,
    x2[0] == -2.04119,
    y2[0] == 0.898024,
    z2[0] == 0}, {x1,x2, y1,y2, z1,z2}, {t, 0, 50}];

So I changed the curly braces to parentheses, as well as added the correct dependent variables in the list at the bottom. Does that work?

It fixed the error but nothing plots:

ParametricPlot3D[
 Evaluate[{x1[t], y1[t], z1[t], x2[t], y2[t], z2[t]} /. s], {t, 0, 
  50}, Boxed -> False, PlotRange -> All, PlotStyle -> {Red}]

 

[Ackbach]

Try something simpler: a 1-D plot of just x2[t]/.s:

Plot[x1[t]/.s,{t,0,50}]

Does that plot?

 

[Dustinsfl]

Try something simpler: a 1-D plot of just x2[t]/.s:

Plot[x1[t]/.s,{t,0,50}]

Does that plot?

I am working on making a little setup that evaluates trajectories for 2 body and restricted 3 body problem. That is why I wanted to change the 2nd order equation of motion for planetary bodies in two 1st order equations.

 

[Ackbach]

Well, I understand that you want to plot a parametric 3D plot, but I'm just trying to debug your code. Start small, and build up to the big plot.

 

[Dustinsfl]

Well, I understand that you want to plot a parametric 3D plot, but I'm just trying to debug your code. Start small, and build up to the big plot.

I have done many of smaller plots. You can view my notes in the ODE section to see. Everything seems correct so I don't see the issue.

That smaller plot won't run.

 

[Ackbach]

I'm a little unclear what the \[Mu] notation means. Why not try this:

ClearAll["Global`*"]
Mu = 398600;
s = NDSolve[{x1'[t] == x2[t],
y1'[t] == y2[t],
z1'[t] == z2[t],
x2'[t] == -Mu*x1[t]/(x1[t]^2 + y1[t]^2 + z1[t]^2)^(3/2),
y2'[t] == -Mu*y1[t]/(x1[t]^2 + y1[t]^2 + z1[t]^2)^(3/2),
z2'[t] == -Mu*z1[t]/(x1[t]^2 + y1[t]^2 + z1[t]^2)^(3/2),
x1[0] == -201000*Sqrt[3],
y1[0] == 201000,
z1[0] == 0,
x2[0] == -2.04119,
y2[0] == 0.898024,
z2[0] == 0}, {x1,x2,y1,y2,z1,z2}, {t, 0, 50}];

Does a small plot work on this?

 

[Dustinsfl]

I'm a little unclear what the \[Mu] notation means. Why not try this:

ClearAll["Global`*"]
Mu = 398600;
s = NDSolve[{x1'[t] == x2[t],
y1'[t] == y2[t],
z1'[t] == z2[t],
x2'[t] == -Mu*x1[t]/(x1[t]^2 + y1[t]^2 + z1[t]^2)^(3/2),
y2'[t] == -Mu*y1[t]/(x1[t]^2 + y1[t]^2 + z1[t]^2)^(3/2),
z2'[t] == -Mu*z1[t]/(x1[t]^2 + y1[t]^2 + z1[t]^2)^(3/2),
x1[0] == -201000*Sqrt[3],
y1[0] == 201000,
z1[0] == 0,
x2[0] == -2.04119,
y2[0] == 0.898024,
z2[0] == 0}, {x1,x2,y1,y2,z1,z2}, {t, 0, 50}];

Does a small plot work on this?

\[Mu] = $\mu$ symbol in Mathematica

 

[Ackbach]

Well, my only advice is to start stripping things out of your model (like dimensions) until you get something that works. Then start adding things back in.

 

[Dustinsfl]

Well, my only advice is to start stripping things out of your model (like dimensions) until you get something that works. Then start adding things back in.

The problem was t. Since I am dealing with space flight, t of 250 is only 250 seconds. Taking t > 1million yields results.