How can one plot a three-dimensional plot of a differential equation system of the following to show the trajectories in mathematica:
$x' = yz,~ y' = -2xz,~ z' = xy$
I tried using VectorPlot3D
and ParametricPlot3D
How can one plot a three-dimensional plot of a differential equation system of the following to show the trajectories in mathematica:
$x' = yz,~ y' = -2xz,~ z' = xy$
I tried using VectorPlot3D
and ParametricPlot3D
How about like so, parameterizing initial conditions by spherical angles $\theta$ and $\phi$:
The copy-paste-ready code:
Traj[\[Theta]_, \[Phi]_, tmax_] :=
Module[{sol}, {sol} =
NDSolve[And @@ {x'[t] == y[t] z[t], y'[t] == -2 x[t] z[t],
z'[t] == x[t] y[t], x[0] == Sin[\[Theta]] Cos[\[Phi]],
y[0] == Sin[\[Theta]] Sin[\[Phi]], z[0] == Cos[\[Theta]]}, {x,
y, z}, {t, 0, tmax}];
sol]
Show[ParametricPlot3D[{x[t], y[t], z[t]} /. {Traj[Pi/5, Pi/3, 7],
Traj[3 Pi/5, Pi/3, 7], Traj[2 Pi/5, Pi/7, 7]}, {t, 0, 7},
PlotRange -> {{-1, 1}, {-1, 1}, {-1, 1}}, Evaluated -> True] /.
Line -> Tube, Graphics3D[{Sphere[{0, 0, 0}, 1]}]]