3 added 227 characters in body
source | link
plot = StreamPlot[{y, -Sin[x]}, {x, -Pi, Pi}, {y, -3, 3},  Frame -> None,  
          Epilog -> {PointSize -> Large, Point[{{0, 0}, {π, 0}, {-π, 0}}]}, 
          StreamPoints -> Fine,  AspectRatio -> 0.8]

Try this:

First[Normal@plot] /.  a_Arrow :> (
                        a /. {x_Real, y_Real} :> {Cos[x], Sin[x], y}
                                  ) // Graphics3D

enter image description here

You can add Cylinder if you want:

Show[ %, 
      Graphics3D@{Opacity@.7, LightBlue, Cylinder[{{0, 0, -3}, {0, 0, 3}}]}
    ]

enter image description here

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

Try this:

First[Normal@plot] /.  a_Arrow :> (
                        a /. {x_Real, y_Real} :> {Cos[x], Sin[x], y}
                                  ) // Graphics3D

enter image description here

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

Try this:

First[Normal@plot] /.  a_Arrow :> (
                        a /. {x_Real, y_Real} :> {Cos[x], Sin[x], y}
                                  ) // Graphics3D

enter image description here

You can add Cylinder if you want:

Show[ %, 
      Graphics3D@{Opacity@.7, LightBlue, Cylinder[{{0, 0, -3}, {0, 0, 3}}]}
    ]

enter image description here

2 deleted 8 characters in body
source | link
plot = StreamPlot[{y, -Sin[x]}, {x, -Pi, Pi}, {y, -3, 3},  Frame -> None,  
          Epilog -> {PointSize -> Large, Point[{{0, 0}, {\[Pi]π, 0}, {-\[Pi]π, 0}}]}, 
          StreamPoints -> Fine,  AspectRatio -> 0.8]

Try this:

First[Normal@plot] /.  a_Arrow :> (
                        a /. {x_Real, y_Real} :> {Cos[x], Sin[x], y}
                                  ) // Graphics3D

enter image description here

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

Try this:

First[Normal@plot] /.  a_Arrow :> (
                        a /. {x_Real, y_Real} :> {Cos[x], Sin[x], y}
                                  ) // Graphics3D

enter image description here

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

Try this:

First[Normal@plot] /.  a_Arrow :> (
                        a /. {x_Real, y_Real} :> {Cos[x], Sin[x], y}
                                  ) // Graphics3D

enter image description here

1
source | link

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

Try this:

First[Normal@plot] /.  a_Arrow :> (
                        a /. {x_Real, y_Real} :> {Cos[x], Sin[x], y}
                                  ) // Graphics3D

enter image description here