How to plot on a curved plane? [duplicate] The 2019 Stack Overflow Developer Survey Results Are InPhase portrait on a cylinderMap a 3D plot into planePlot points, line and plane in one 3D plotPlot sets in the complex planeHow to plot in the complex plane?How to plot list of numbers in the complex plane?Adding a curved line to a DensityPlotHow to plot a spiral on a plane?IRR Plot on Complex PlanePlot a “curved stroke” graphicPlane surface data plot

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How to plot on a curved plane? [duplicate]



The 2019 Stack Overflow Developer Survey Results Are InPhase portrait on a cylinderMap a 3D plot into planePlot points, line and plane in one 3D plotPlot sets in the complex planeHow to plot in the complex plane?How to plot list of numbers in the complex plane?Adding a curved line to a DensityPlotHow to plot a spiral on a plane?IRR Plot on Complex PlanePlot a “curved stroke” graphicPlane surface data plot










4












$begingroup$



This question already has an answer here:



  • Phase portrait on a cylinder

    2 answers



I'm ploting the phase space of a pendulum problem using a symplectic Euler scheme.



$qquad H = frac12p^2 - cos q$, where $dotp=-sin q$ and $dotq=p$



h=0.2; (*time step*)
p[0]=0.0; (*initial conditions*)
q[0]=0.5;

p[i_] := p[i] = p[i - 1] - h*Sin[q[i - 1]];
q[i_] := q[i] = q[i - 1] + h*p[i - 1] - h^2*Sin[q[i - 1]];

ListPlot[Table[p[i], q[i], i, 0, 100], Frame -> True]


gives



phase space plot



Since the vector field is $2π$-periodic in q, it is natural to consider q as a variable on the circle $S^1$, I'd expect it to look something like



enter image description here



Any suggest how to do it?










share|improve this question











$endgroup$



marked as duplicate by Michael E2 plotting
Users with the  plotting badge can single-handedly close plotting questions as duplicates and reopen them as needed.

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This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

















  • $begingroup$
    There is no such thing as a "curved plane". If want to plot on a 2-manifold, please give a description of the manifold in Wolfram Language code.
    $endgroup$
    – m_goldberg
    Apr 6 at 5:52










  • $begingroup$
    @MichaelE2 it is indeed a duplicate, I'm happy with the solution provided, feel free to close it.
    $endgroup$
    – Gvxfjørt
    Apr 8 at 1:46















4












$begingroup$



This question already has an answer here:



  • Phase portrait on a cylinder

    2 answers



I'm ploting the phase space of a pendulum problem using a symplectic Euler scheme.



$qquad H = frac12p^2 - cos q$, where $dotp=-sin q$ and $dotq=p$



h=0.2; (*time step*)
p[0]=0.0; (*initial conditions*)
q[0]=0.5;

p[i_] := p[i] = p[i - 1] - h*Sin[q[i - 1]];
q[i_] := q[i] = q[i - 1] + h*p[i - 1] - h^2*Sin[q[i - 1]];

ListPlot[Table[p[i], q[i], i, 0, 100], Frame -> True]


gives



phase space plot



Since the vector field is $2π$-periodic in q, it is natural to consider q as a variable on the circle $S^1$, I'd expect it to look something like



enter image description here



Any suggest how to do it?










share|improve this question











$endgroup$



marked as duplicate by Michael E2 plotting
Users with the  plotting badge can single-handedly close plotting questions as duplicates and reopen them as needed.

StackExchange.ready(function()
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Apr 8 at 2:38


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

















  • $begingroup$
    There is no such thing as a "curved plane". If want to plot on a 2-manifold, please give a description of the manifold in Wolfram Language code.
    $endgroup$
    – m_goldberg
    Apr 6 at 5:52










  • $begingroup$
    @MichaelE2 it is indeed a duplicate, I'm happy with the solution provided, feel free to close it.
    $endgroup$
    – Gvxfjørt
    Apr 8 at 1:46













4












4








4





$begingroup$



This question already has an answer here:



  • Phase portrait on a cylinder

    2 answers



I'm ploting the phase space of a pendulum problem using a symplectic Euler scheme.



$qquad H = frac12p^2 - cos q$, where $dotp=-sin q$ and $dotq=p$



h=0.2; (*time step*)
p[0]=0.0; (*initial conditions*)
q[0]=0.5;

p[i_] := p[i] = p[i - 1] - h*Sin[q[i - 1]];
q[i_] := q[i] = q[i - 1] + h*p[i - 1] - h^2*Sin[q[i - 1]];

ListPlot[Table[p[i], q[i], i, 0, 100], Frame -> True]


gives



phase space plot



Since the vector field is $2π$-periodic in q, it is natural to consider q as a variable on the circle $S^1$, I'd expect it to look something like



enter image description here



Any suggest how to do it?










share|improve this question











$endgroup$





This question already has an answer here:



  • Phase portrait on a cylinder

    2 answers



I'm ploting the phase space of a pendulum problem using a symplectic Euler scheme.



$qquad H = frac12p^2 - cos q$, where $dotp=-sin q$ and $dotq=p$



h=0.2; (*time step*)
p[0]=0.0; (*initial conditions*)
q[0]=0.5;

p[i_] := p[i] = p[i - 1] - h*Sin[q[i - 1]];
q[i_] := q[i] = q[i - 1] + h*p[i - 1] - h^2*Sin[q[i - 1]];

ListPlot[Table[p[i], q[i], i, 0, 100], Frame -> True]


gives



phase space plot



Since the vector field is $2π$-periodic in q, it is natural to consider q as a variable on the circle $S^1$, I'd expect it to look something like



enter image description here



Any suggest how to do it?





This question already has an answer here:



  • Phase portrait on a cylinder

    2 answers







plotting






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited Apr 6 at 5:56









m_goldberg

88.6k873200




88.6k873200










asked Apr 6 at 2:13









GvxfjørtGvxfjørt

986




986




marked as duplicate by Michael E2 plotting
Users with the  plotting badge can single-handedly close plotting questions as duplicates and reopen them as needed.

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Apr 8 at 2:38


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.









marked as duplicate by Michael E2 plotting
Users with the  plotting badge can single-handedly close plotting questions as duplicates and reopen them as needed.

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Apr 8 at 2:38


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.













  • $begingroup$
    There is no such thing as a "curved plane". If want to plot on a 2-manifold, please give a description of the manifold in Wolfram Language code.
    $endgroup$
    – m_goldberg
    Apr 6 at 5:52










  • $begingroup$
    @MichaelE2 it is indeed a duplicate, I'm happy with the solution provided, feel free to close it.
    $endgroup$
    – Gvxfjørt
    Apr 8 at 1:46
















  • $begingroup$
    There is no such thing as a "curved plane". If want to plot on a 2-manifold, please give a description of the manifold in Wolfram Language code.
    $endgroup$
    – m_goldberg
    Apr 6 at 5:52










  • $begingroup$
    @MichaelE2 it is indeed a duplicate, I'm happy with the solution provided, feel free to close it.
    $endgroup$
    – Gvxfjørt
    Apr 8 at 1:46















$begingroup$
There is no such thing as a "curved plane". If want to plot on a 2-manifold, please give a description of the manifold in Wolfram Language code.
$endgroup$
– m_goldberg
Apr 6 at 5:52




$begingroup$
There is no such thing as a "curved plane". If want to plot on a 2-manifold, please give a description of the manifold in Wolfram Language code.
$endgroup$
– m_goldberg
Apr 6 at 5:52












$begingroup$
@MichaelE2 it is indeed a duplicate, I'm happy with the solution provided, feel free to close it.
$endgroup$
– Gvxfjørt
Apr 8 at 1:46




$begingroup$
@MichaelE2 it is indeed a duplicate, I'm happy with the solution provided, feel free to close it.
$endgroup$
– Gvxfjørt
Apr 8 at 1:46










1 Answer
1






active

oldest

votes


















7












$begingroup$


h = 0.2;
p[0, a_] := 0;
q[0, a_] := a
p[i_, a_] := p[i, a] = p[i - 1, a] - h*Sin[q[i - 1, a]];
q[i_, a_] :=
q[i, a] = q[i - 1, a] + h*p[i - 1, a] - h^2*Sin[q[i - 1, a]];




plots = Table[
ListPointPlot3D[
Table[Sin[q[i, a]], Cos[q[i, a]], p[i, a], i, 0, 100],
PlotStyle -> PointSize[0.008],
PlotRange -> -1, 1, -1, 1, -3, 3], a, 0.5, 3, 0.5];



Show[plots,
Graphics3D[Opacity[0.1], Cylinder[0, 0, -3, 0, 0, 3]]]



enter image description here






share|improve this answer









$endgroup$



















    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    7












    $begingroup$


    h = 0.2;
    p[0, a_] := 0;
    q[0, a_] := a
    p[i_, a_] := p[i, a] = p[i - 1, a] - h*Sin[q[i - 1, a]];
    q[i_, a_] :=
    q[i, a] = q[i - 1, a] + h*p[i - 1, a] - h^2*Sin[q[i - 1, a]];




    plots = Table[
    ListPointPlot3D[
    Table[Sin[q[i, a]], Cos[q[i, a]], p[i, a], i, 0, 100],
    PlotStyle -> PointSize[0.008],
    PlotRange -> -1, 1, -1, 1, -3, 3], a, 0.5, 3, 0.5];



    Show[plots,
    Graphics3D[Opacity[0.1], Cylinder[0, 0, -3, 0, 0, 3]]]



    enter image description here






    share|improve this answer









    $endgroup$

















      7












      $begingroup$


      h = 0.2;
      p[0, a_] := 0;
      q[0, a_] := a
      p[i_, a_] := p[i, a] = p[i - 1, a] - h*Sin[q[i - 1, a]];
      q[i_, a_] :=
      q[i, a] = q[i - 1, a] + h*p[i - 1, a] - h^2*Sin[q[i - 1, a]];




      plots = Table[
      ListPointPlot3D[
      Table[Sin[q[i, a]], Cos[q[i, a]], p[i, a], i, 0, 100],
      PlotStyle -> PointSize[0.008],
      PlotRange -> -1, 1, -1, 1, -3, 3], a, 0.5, 3, 0.5];



      Show[plots,
      Graphics3D[Opacity[0.1], Cylinder[0, 0, -3, 0, 0, 3]]]



      enter image description here






      share|improve this answer









      $endgroup$















        7












        7








        7





        $begingroup$


        h = 0.2;
        p[0, a_] := 0;
        q[0, a_] := a
        p[i_, a_] := p[i, a] = p[i - 1, a] - h*Sin[q[i - 1, a]];
        q[i_, a_] :=
        q[i, a] = q[i - 1, a] + h*p[i - 1, a] - h^2*Sin[q[i - 1, a]];




        plots = Table[
        ListPointPlot3D[
        Table[Sin[q[i, a]], Cos[q[i, a]], p[i, a], i, 0, 100],
        PlotStyle -> PointSize[0.008],
        PlotRange -> -1, 1, -1, 1, -3, 3], a, 0.5, 3, 0.5];



        Show[plots,
        Graphics3D[Opacity[0.1], Cylinder[0, 0, -3, 0, 0, 3]]]



        enter image description here






        share|improve this answer









        $endgroup$




        h = 0.2;
        p[0, a_] := 0;
        q[0, a_] := a
        p[i_, a_] := p[i, a] = p[i - 1, a] - h*Sin[q[i - 1, a]];
        q[i_, a_] :=
        q[i, a] = q[i - 1, a] + h*p[i - 1, a] - h^2*Sin[q[i - 1, a]];




        plots = Table[
        ListPointPlot3D[
        Table[Sin[q[i, a]], Cos[q[i, a]], p[i, a], i, 0, 100],
        PlotStyle -> PointSize[0.008],
        PlotRange -> -1, 1, -1, 1, -3, 3], a, 0.5, 3, 0.5];



        Show[plots,
        Graphics3D[Opacity[0.1], Cylinder[0, 0, -3, 0, 0, 3]]]



        enter image description here







        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered Apr 6 at 6:10









        ulviulvi

        1,176612




        1,176612













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