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How to plot on a curved plane?
Phase 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
$begingroup$
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
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
Any suggest how to do it?
plotting
edited 19 hours ago
m_goldberg
88.2k872199
asked 22 hours ago
GvxfjørtGvxfjørt
986
$endgroup$
add a comment |
$begingroup$
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
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
Any suggest how to do it?
plotting
edited 19 hours ago
m_goldberg
88.2k872199
asked 22 hours ago
GvxfjørtGvxfjørt
986
$endgroup$
$begingroup$
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
19 hours ago
$begingroup$
Possible duplicate: mathematica.stackexchange.com/questions/64407/…
$endgroup$
– Michael E2
2 hours ago
add a comment |
$begingroup$
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
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
Any suggest how to do it?
plotting
edited 19 hours ago
m_goldberg
88.2k872199
asked 22 hours ago
GvxfjørtGvxfjørt
986
$endgroup$
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
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
Any suggest how to do it?
plotting
plotting
edited 19 hours ago
m_goldberg
88.2k872199
asked 22 hours ago
GvxfjørtGvxfjørt
986
edited 19 hours ago
m_goldberg
88.2k872199
asked 22 hours ago
GvxfjørtGvxfjørt
986
edited 19 hours ago
m_goldberg
88.2k872199
edited 19 hours ago
m_goldberg
88.2k872199
edited 19 hours ago
m_goldberg
88.2k872199
88.2k872199
asked 22 hours ago
GvxfjørtGvxfjørt
986
asked 22 hours ago
GvxfjørtGvxfjørt
986
asked 22 hours ago
GvxfjørtGvxfjørt
986
986
$begingroup$
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
19 hours ago
$begingroup$
Possible duplicate: mathematica.stackexchange.com/questions/64407/…
$endgroup$
– Michael E2
2 hours ago
add a comment |
$begingroup$
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
19 hours ago
$begingroup$
Possible duplicate: mathematica.stackexchange.com/questions/64407/…
$endgroup$
– Michael E2
2 hours ago
$begingroup$
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
19 hours ago
$begingroup$
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
19 hours ago
$begingroup$
Possible duplicate: mathematica.stackexchange.com/questions/64407/…
$endgroup$
– Michael E2
2 hours ago
$begingroup$
Possible duplicate: mathematica.stackexchange.com/questions/64407/…
$endgroup$
– Michael E2
2 hours ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
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]]]
answered 18 hours ago
ulviulvi
1,166612
$endgroup$
add a comment |
Your Answer
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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]]]
answered 18 hours ago
ulviulvi
1,166612
$endgroup$
add a comment |
$begingroup$
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]]]
answered 18 hours ago
ulviulvi
1,166612
$endgroup$
add a comment |
$begingroup$
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]]]
answered 18 hours ago
ulviulvi
1,166612
$endgroup$
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]]]
answered 18 hours ago
ulviulvi
1,166612
answered 18 hours ago
ulviulvi
1,166612
answered 18 hours ago
ulviulvi
1,166612
answered 18 hours ago
ulviulvi
1,166612
1,166612
add a comment |
add a comment |
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$begingroup$
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
19 hours ago
$begingroup$
Possible duplicate: mathematica.stackexchange.com/questions/64407/…
$endgroup$
– Michael E2
2 hours ago