4 added 2 characters in body edited Aug 22 '14 at 0:10 m_goldberg 91.6k88 gold badges7575 silver badges209209 bronze badges 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., q == 0, y' == 50., q' == 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}] 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"}]] 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., q == 0, y' == 50., q' == 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}] 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"}]] 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., q == 0, y' == 50., q' == 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}] 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"}]] 3 inserted code for 2nd plot edited Aug 22 '14 at 0:04 m_goldberg 91.6k88 gold badges7575 silver badges209209 bronze badges 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., q == 0, y' == 50., q' == 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}]  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"}]] 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., q == 0, y' == 50., q' == 15.}, {q, y}, {t, 0., 10.}]; f[t_] = {q[t], y[t]} /. numSoln; ParametricPlot[f[t], {t, 0., 10.}] 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., q == 0, y' == 50., q' == 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}] 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"}]] 2 clarification edited Aug 21 '14 at 23:34 m_goldberg 91.6k88 gold badges7575 silver badges209209 bronze badges 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., q == 0, y' == 50., q' == 15.}, {q, y}, {t, 0., 10.}]; f[t_] = {q[t], y[t]} /. numSoln; ParametricPlot[f[t], {t, 0., 10.}] 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., q == 0, y' == 50., q' == 15.}, {q, y}, {t, 0., 10.}]; f[t_] = {q[t], y[t]} /. numSoln; ParametricPlot[f[t], {t, 0., 10.}] 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., q == 0, y' == 50., q' == 15.}, {q, y}, {t, 0., 10.}]; f[t_] = {q[t], y[t]} /. numSoln; ParametricPlot[f[t], {t, 0., 10.}] So f is the numerical approximation to the path function of the particle. 1 answered Aug 21 '14 at 16:03 m_goldberg 91.6k88 gold badges7575 silver badges209209 bronze badges