# Draw phase portrait with StreamPlot on a sphere [closed]

I would like to draw this phase portrait using StreamPlot on sphere as in this picture like that

In fact, i have seen this for the classical pendulum defined by enter link description here

StreamPlot[{y, -Sin[x]}, {x, -5, 5}, {y, -3, 3}, Frame -> None, StreamPoints -> Fine, AspectRatio -> 0.8, Epilog -> {PointSize -> Large, Point[{{0, 0}, {\[Pi], 0}, {-\[Pi], 0}}]}]


It have defined cyl enter link description here with a complicated transformation on that.

• On a sphere or on a cylinder? Dec 14, 2021 at 22:57
• What do x and y represent? To draw a phase portrait on a sphere you need a vector field (or ODE) on a sphere. In the cylinder example, the field/ODE is invariant under the transformation $x \mapsto x+2\pi$, which allows one to map the vector field $(\dot x, \dot y) = (y, -\sin x)$ on the plane to a vector field on a cylinder. There's no such natural mapping onto the sphere, so you would have to define one. Dec 15, 2021 at 3:04

## 1 Answer

texture =
StreamPlot[{y, -Sin[x]}, {x, -5, 5}, {y, -3, 3}, Frame -> None,
StreamPoints -> Fine, AspectRatio -> 0.8,
Epilog -> {PointSize -> Large,
Point[{{0, 0}, {π, 0}, {-π, 0}}]}]
ParametricPlot3D[
FromSphericalCoordinates[{1, θ, φ}] //
Evaluate, {θ, 0, Pi}, {φ, 0, 2 Pi},
PlotPoints -> 50, Boxed -> False, Axes -> None, Mesh -> None,
PlotStyle -> Texture[texture], TextureCoordinateScaling -> True]


• many thanks, could you modify this in order to get a sphere as above and draw a data points on it. Dec 15, 2021 at 11:56
• In my personal opinion you try to answer an incorrect question which makes no sense. It's unclear to me what StreamPlot on the sphere is at all Dec 15, 2021 at 12:16
• @user64494 He wan to draw a portrait onto a sphere instead of a vector fields on sphere,so we need not consider vector field. Dec 15, 2021 at 12:22
• @cvgmt: It's unclear what portrait should be drawn. I repeat you try to answer an ill-posed question (see the Michael E2's comment to the question). Don't hesitate to ask for further explanation in need. Dec 15, 2021 at 12:24