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You can get a path function directly from the solution of your ODEs.

I don't understand your ODE's, so I'm going to work with a much simpler system, which gives the path of particle moving under constant gravity in a vacuum.

g = -9.8;
numSoln = 
  NDSolve[{
       y''[t] == g, q''[t] == 0., 
       y[0] == 0., q[0] == 0, 
       y'[0] == 50., q'[0] == 15.}, 
    {q, y}, {t, 0., 10.}];

From numSoln, the numerical solution of the ODEs, the approximate path function is given by

f[t_] = {q[t], y[t]} /. numSoln;

The above expression for f is independent of the precise form of the ODEs, so it is applicable to your problem as well. The following plot is made to visually confirms the result.

ParametricPlot[f[t], {t, 0., 10.}, AxesLabel -> {q, y}]

path

The components q and y as functions of t can also be recovered from f.

Plot[Evaluate@f[t]Plot[Evaluate @ f[t], {t, 0., 10.},
  AxesLabel -> {t, None},
  PlotLegends -> SwatchLegend[Automatic, {"q", "y"}]]

f[t]

You can get a path function directly from the solution of your ODEs.

I don't understand your ODE's, so I'm going to work with a much simpler system, which gives the path of particle moving under constant gravity in a vacuum.

g = -9.8;
numSoln = 
  NDSolve[{
       y''[t] == g, q''[t] == 0., 
       y[0] == 0., q[0] == 0, 
       y'[0] == 50., q'[0] == 15.}, 
    {q, y}, {t, 0., 10.}];

From numSoln, the numerical solution of the ODEs, the approximate path function is given by

f[t_] = {q[t], y[t]} /. numSoln;

The above expression for f is independent of the precise form of the ODEs, so it is applicable to your problem as well. The following plot is made to visually confirms the result.

ParametricPlot[f[t], {t, 0., 10.}, AxesLabel -> {q, y}]

path

The components q and y as functions of t can also be recovered from f.

Plot[Evaluate@f[t], {t, 0., 10.},
  AxesLabel -> {t, None},
  PlotLegends -> SwatchLegend[Automatic, {"q", "y"}]]

f[t]

You can get a path function directly from the solution of your ODEs.

I don't understand your ODE's, so I'm going to work with a much simpler system, which gives the path of particle moving under constant gravity in a vacuum.

g = -9.8;
numSoln = 
  NDSolve[{
       y''[t] == g, q''[t] == 0., 
       y[0] == 0., q[0] == 0, 
       y'[0] == 50., q'[0] == 15.}, 
    {q, y}, {t, 0., 10.}];

From numSoln, the numerical solution of the ODEs, the approximate path function is given by

f[t_] = {q[t], y[t]} /. numSoln;

The above expression for f is independent of the precise form of the ODEs, so it is applicable to your problem as well. The following plot is made to visually confirms the result.

ParametricPlot[f[t], {t, 0., 10.}, AxesLabel -> {q, y}]

path

The components q and y as functions of t can also be recovered from f.

Plot[Evaluate @ f[t], {t, 0., 10.},
  AxesLabel -> {t, None},
  PlotLegends -> SwatchLegend[Automatic, {"q", "y"}]]

f[t]

3 inserted code for 2nd plot
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You can get a path function directly from the solution of your ODEs.

I don't understand your ODE's, so I'm going to work with a much simpler system, which gives the path of particle moving under constant gravity in a vacuum. What I do here should directly apply to your problem, however.

g = -9.8;
numSoln = 
  NDSolve[{
       y''[t] == g, q''[t] == 0., 
       y[0] == 0., q[0] == 0, 
       y'[0] == 50., q'[0] == 15.}, 
    {q, y}, {t, 0., 10.}];

From numSoln, the numerical solution of the ODEs, the approximate path function is given by

f[t_] = {q[t], y[t]} /. numSoln;

The above expression for f is independent of the precise form of the ODEs, so it is applicable to your problem as well. The following plot is made to visually confirms the result.

ParametricPlot[f[t], {t, 0., 10.}, AxesLabel -> {q, y}]

pathpath

SoThe components fq is the numerical approximation to the path functionand y as functions of the particlet can also be recovered from f.

Plot[Evaluate@f[t], {t, 0., 10.},
  AxesLabel -> {t, None},
  PlotLegends -> SwatchLegend[Automatic, {"q", "y"}]]

f[t]

You can get a path function directly from the solution of your ODEs.

I don't understand your ODE's, so I'm going to work with a much simpler system, which gives the path of particle moving under constant gravity in a vacuum. What I do here should directly apply to your problem, however.

g = -9.8;
numSoln = 
  NDSolve[{
       y''[t] == g, q''[t] == 0., 
       y[0] == 0., q[0] == 0, 
       y'[0] == 50., q'[0] == 15.}, 
    {q, y}, {t, 0., 10.}];
f[t_] = {q[t], y[t]} /. numSoln;
ParametricPlot[f[t], {t, 0., 10.}]

path

So f is the numerical approximation to the path function of the particle.

You can get a path function directly from the solution of your ODEs.

I don't understand your ODE's, so I'm going to work with a much simpler system, which gives the path of particle moving under constant gravity in a vacuum.

g = -9.8;
numSoln = 
  NDSolve[{
       y''[t] == g, q''[t] == 0., 
       y[0] == 0., q[0] == 0, 
       y'[0] == 50., q'[0] == 15.}, 
    {q, y}, {t, 0., 10.}];

From numSoln, the numerical solution of the ODEs, the approximate path function is given by

f[t_] = {q[t], y[t]} /. numSoln;

The above expression for f is independent of the precise form of the ODEs, so it is applicable to your problem as well. The following plot is made to visually confirms the result.

ParametricPlot[f[t], {t, 0., 10.}, AxesLabel -> {q, y}]

path

The components q and y as functions of t can also be recovered from f.

Plot[Evaluate@f[t], {t, 0., 10.},
  AxesLabel -> {t, None},
  PlotLegends -> SwatchLegend[Automatic, {"q", "y"}]]

f[t]

2 clarification
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You can get a path function directly from the solution of your ODEs.

I don't understand your ODE's, so I'm going to work with a much simpler system, which gives the path of particle moving under constant gravity in a vacuum. What I do here should directly apply to your problem, however.

g = -9.8;
numSoln = 
  NDSolve[{
       y''[t] == g, q''[t] == 0., 
       y[0] == 0., q[0] == 0, 
       y'[0] == 50., q'[0] == 15.}, 
    {q, y}, {t, 0., 10.}];
f[t_] = {q[t], y[t]} /. numSoln;
ParametricPlot[f[t], {t, 0., 10.}]

path

So f is the numerical approximation to the path function of the particle.

You can get a path function directly from the solution of your ODEs.

I don't understand your ODE's, so I'm going to work with a much simpler system, which gives the path of particle moving under constant gravity in a vacuum. What I do here should directly apply to your problem, however.

g = -9.8;
numSoln = 
  NDSolve[{
       y''[t] == g, q''[t] == 0., 
       y[0] == 0., q[0] == 0, 
       y'[0] == 50., q'[0] == 15.}, 
    {q, y}, {t, 0., 10.}];
f[t_] = {q[t], y[t]} /. numSoln;
ParametricPlot[f[t], {t, 0., 10.}]

path

So f is the path function of the particle.

You can get a path function directly from the solution of your ODEs.

I don't understand your ODE's, so I'm going to work with a much simpler system, which gives the path of particle moving under constant gravity in a vacuum. What I do here should directly apply to your problem, however.

g = -9.8;
numSoln = 
  NDSolve[{
       y''[t] == g, q''[t] == 0., 
       y[0] == 0., q[0] == 0, 
       y'[0] == 50., q'[0] == 15.}, 
    {q, y}, {t, 0., 10.}];
f[t_] = {q[t], y[t]} /. numSoln;
ParametricPlot[f[t], {t, 0., 10.}]

path

So f is the numerical approximation to the path function of the particle.

1
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