Equilibrium solution for y'=3-2y is at y=3/2 and I would like to add the line y=3/2 to direction field plotted using VectorPlot function. How to do?
The additional code below does it.
points = {{0, 0}, {1, 0}, {2, 0}, {0, 1}, {1, 1}, {2, 1}, {0, 2}, {1,
2}, {2, 2}};
datplot =
VectorPlot[{1, 3 - 2 y}, {x, 0, 2}, {y, 0, 2},
VectorPoints -> points, VectorScale -> {Automatic, Automatic, None},
Epilog -> {Red, PointSize[Medium], Point[points]}];
fitplot = Plot[y = 3/2, {y, 0, 2}];
{Show[datplot, fitplot]}
Mary A. Marion
Change
Epilog -> {Red, PointSize[Medium], Point[points]}
to
Epilog -> {Red, PointSize[Medium], Point[points], Line[{{0,3/2},{2,3/2}}]}
The following code will compute the solution*:
points = {{0, 0}, {1, 0}, {2, 0}, {0, 1}, {1, 1}, {2, 1},
{0, 2}, {1,2}, {2, 2}};
datplot =
VectorPlot[{1, 3 - 2 y}, {x, 0, 2}, {y, 0, 2},
VectorPoints -> points, VectorScale -> {Automatic, Automatic, None},
Epilog -> {Red, PointSize[Medium], Point[points],
Line[{{0, 3/2}, {2, 3/2}}]}]
See Bill's input above.
Currently I am trying to graph the sin(x) function and a function named myPolys which is the taylor polynomial of sin(x) as it is equal to
myPolys =
Table[Table[(-1)^((j - 1)/2) x^j/Factorial[j], {j, 1, h, 2}], {h, 1,
19, 2}];
How can I use manipulate to graph both functions so that each part of myPolys is graphed
My graphing code so far:
Manipulate[Plot[{Sin[x], myPolys[[n]]}, {x, -10, 10},
PlotRange -> {-5, 5}], {n, 1, Length[myPolys], 1}];
currently for each iteration of n, myPolys is graphed as separate
x and then x & -(x^3)/3! and then x & -(x^3)/3! & x^5/5! (all are plotted separate o the same graph )
The graph I'm trying to achieve is that for n=1 sin(x) should be plotted and x from myPoly should be plotted, for n=2 it continues and graphs x-(x^3/3!) (instead of plotting, for n=2, x and -x^3/3! seperately) and so on and so forth until n reaches 10.
My graph at the moment:
The graph I'm hoping for:
myPolys = Table[Sum[(-1)^((j - 1)/2) x^j/Factorial[j],
{j, 1, h, 2}], {h, 1, 19, 2}];
Manipulate[Plot[{Sin[x], Evaluate#Take[myPolys, n]},
{x, -10, 10}, PlotRange -> {-5, 5}], {n, 1, Length[myPolys], 1}]
Or, in more functional style.
Clear[myPolys]
myPolys[n_] := Table[Sum[(-1)^((j - 1)/2) x^j/Factorial[j],
{j, 1, h, 2}], {h, 1, 2 n - 1, 2}]
Manipulate[Plot[{Sin[x], Evaluate#myPolys[n]},
{x, -10, 10}, PlotRange -> {-5, 5}], {n, 1, 10, 1}]
And with legend.
myLabels[n_] := Table[Sum[(-1)^((j - 1)/2) x^j/ToString[j] <> "!",
{j, 1, h, 2}], {h, 1, 2 n - 1, 2}]
Manipulate[Plot[{Sin[x], Evaluate#myPolys[n]},
{x, -10, 10}, PlotRange -> {-5, 5},
PlotLegends -> Placed[PointLegend[
Rest#Array[ColorData[97], n + 1], HoldForm /# myLabels[n],
LegendMarkers -> {"\[Tilde]", 30}], Left]], {n, 1, 10, 1}]
I suppose you know there is the built in Series you can use..
Manipulate[m = n;
Show[{
Plot[Sin[x], {x, -10, 10}, PlotRange -> {-5, 5},
PlotStyle -> {Thick, Red}],
Plot[Evaluate[
Accumulate[List ## Normal#Series[Sin[x], {x, 0, m}]]], {x, -10, 10}]}],
{{n, 3}, 3, 25, 2}]
I have a question about using plot and disk together in one manipulate function in mathematica.
I have this piece of code right now:
Plot[h[t], {t, 0, ttot}, PlotRange -> {0, 30}]
Manipulate[
Plot[
h0 + v0*t - 1/2*g*(t)^2, {t, 0, 10},
PlotRange -> {{-1, 8}, {0, 11.5}}
],
{t, 0, ttot, 0.001}, {m, 0.001, 0.1, 0.001, ImageSize -> Tiny}, {v0,
0, 5, 0.01, ImageSize -> Tiny}, {h0, 0, 10, 0.01, ImageSize -> Tiny}
]
What I want to do is display a disk inside the plot representing a flying object (its position is on the curve, according to actual time and height). How do I do it?
You should show the definitions of the symbols you use : h[t], v0, ttot etc.
My understanding of what you are after :
trajectory[p0_, v0_, a_, t_] = p0 + v0 t - 1/2 a t^2;
x0 = 3;
v0y = 1;
g = 9.81;
ttot = 3;
Manipulate[ParametricPlot[trajectory[{x0, h0}, {v0x, v0y}, {0, g}, t], {t, 0, ttot}, Epilog -> {Disk[trajectory[{x0, h0}, {v0x, v0y}, {0, g}, tcurrent], 0.5]}, PlotRange -> All], {v0x, 0, 5, 0.01}, {h0, 0, 10, 0.01}, {tcurrent, 0, ttot, 0.01}]
I am trying to upgrade some equations that currently are written against Mathematica 5 to get them to work in Mathematica 7.
F = Graphics[
ContourPlot[
x^2 + (2)*y^2 + (-1)*((1)/(3))*x, {x, -1, 1}, {y, -1, 1},
ContourShading -> False, ContourStyle -> {RGBColor[1, 0, 1]},
Contours -> 20, PlotPoints -> 100]];
G = ParametricPlot[{Cos[u], Sin[u]}, {u, 0, 2*Pi},
PlotStyle -> {RGBColor[0, 174/255, 239/255]}];
H = DeleteCases[F, {x_, y_} /; (x^2 + y^2 > 1), 5];
Show[{H, G}, AspectRatio -> Automatic, Frame -> False, Axes -> True,
AxesOrigin -> {0, 0}, AxesLabel -> {x, y}, Ticks -> None]
It should look like this:
, but id does look like this:
and it gives the following error:
Thread::tdlen: Objects of unequal length in
{{},{},{},{},{},{},{},{},{},{},{},{},{},{},{},{},{},{},{},{},{}}+{{},<<21>>,{}}
cannot be combined. >>
and if you hover over the image you get the following in a tooltip:
The specified setting for the option GraphicsBoxOptions, PlotRange cannot be used.
Coordinate index X is out of range for the enclosing GraphicsComplex
there are a lot of those Coordinate ones all with different coordinates.
And the second one I'm having difficulty with is:
P1 = {{(5)/10*Cos[u]*Cos[v], (5)/10*Sin[u]*Cos[v], (5)/10*Sin[v]}, {u,
0, 2*Pi}, {v, -Pi/2, Pi/2}};
P2 = {{(5)/10*Cos[u], 0, (5)/10*Sin[u]}, {u, 0, 2*Pi}};
P3 = {{(5)/10*Cos[u], (5)/10*Sin[u], 0}, {u, 0, 2*Pi}};
P4 = {{0, (5)/10*Cos[u], (5)/10*Sin[u]}, {u, 0, 2*Pi}};
U = {P1, P2, P3, P4};
XL = {{-1, 1}, {-1, 1}, {-1, 1}};
XV = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
XS = {"x", "y", "z"};
f[a_, b_, c_] := {a, 1.1*b[[2]]*c};
g[a_, b_] := {(b*# &) /# a};
T = Text ### MapThread[f, {XS, XL, XV}];
A = Line ### MapThread[g, {XL, XV}];
F = (ParametricPlot3D[Evaluate[Evaluate ## #]][[1]] &) /# U;
OPT = {Boxed -> False, Axes -> False, BoxRatios -> {1, 1, 1}, PlotRange -> XL,
ViewPoint -> {2.4, 1.3, 2},
DisplayFunction ->
Identity};
L = {LightSources -> {{{0.1, 0, 1}, RGBColor[0.68, 0.88, 0.96]}}};
gr1 = (Show[Graphics3D[#], OPT, L] &) /# {{EdgeForm[], F}, {Dashing[{0.03, 0.03}],
GrayLevel[0.7], A}, {T}};
gr2 = DeleteCases[Graphics[Show[Graphics3D[{A, EdgeForm[], F}], OPT,
RenderAll -> False]], {__, _Polygon}, 3];
Show[{gr1, gr2}, AspectRatio -> Automatic]
This one should look like: , but does look like:
which and it gives these errors:
ParametricPlot3D::write: Tag Plus in x^2+y^2 is Protected. >>
Graphics3D::optx : Unknown option RenderAll
Graphics3D::optx : Unknown option LightSources
If I then remove the Unknown options, those errors disappear but it still looks wrong:
Also, if you hover over the last image in mathematica you get the following message repeated several times in a tooltip
Times is not a Graphics3D primitive or directive
Second one, great circles partly hidden, axes partly dashed:
r = 1.01/2; d = 1/(100 r);
v1 = Riffle[
Table[r { Cos[\[Phi]], Sin[\[Phi]], -d}, {\[Phi], 0, 2 \[Pi], (
2 \[Pi])/40.}],
Table[r { Cos[\[Phi]], Sin[\[Phi]], d}, {\[Phi], 0, 2 \[Pi], (
2 \[Pi])/40.}]];
v2 = Riffle[
Table[-r { Cos[\[Phi]], -d, Sin[\[Phi]]}, {\[Phi], 0, 2 \[Pi], (
2 \[Pi])/40.}],
Table[-r { Cos[\[Phi]], d, Sin[\[Phi]]}, {\[Phi], 0, 2 \[Pi], (
2 \[Pi])/40.}]];
v3 = Riffle[
Table[r { -d, Cos[\[Phi]], Sin[\[Phi]]}, {\[Phi], 0, 2 \[Pi], (
2 \[Pi])/40.}],
Table[r { d, Cos[\[Phi]], Sin[\[Phi]]}, {\[Phi], 0, 2 \[Pi], (
2 \[Pi])/40.}]];
lx = {{{1, 0, 0}, {2, 0, 0}}}/2;
ly = {{{0, 1, 0}, {0, 2, 0}}}/2;
lz = {{{0, 0, 1}, {0, 0, 2}}}/2;
A2 = Line ### {lx, ly, lz, -lx, -ly, -lz};
Graphics3D[
{
FaceForm[None, Black], EdgeForm[],
GraphicsComplex[#,
Table[Polygon[Mod[{i, i + 1, i + 3, i + 2}, Length[v], 1]], {i,
1, Length[v] - 1, 2}]] & /# {v1, v2, v3}, {Opacity[0.75],
RGBColor[0.68`, 0.88`, 0.96`], Sphere[{0, 0, 0}, 1/2]},
{Dashing[{0.02, 0.02}], Black, A}, T, A2
},
Boxed -> False,
Lighting -> {{"Directional", RGBColor[0.68`, 0.88`, 0.96`],
ImageScaled#{0.1, 0, 1}}}, BoxRatios -> {1, 1, 1},
PlotRange -> {{-1, 1}, {-1, 1}, {-1, 1}},
BaseStyle -> FontSize -> 14, ViewPoint -> {2.4`, 1.3`, 2},
ViewVertical -> {0, 0, 1}
]
It is a little hard to tell from the picture what you want for the second graphic. Please try this and tell me what is right and what is lacking.
P1 = {{(5)/10*Cos[u]*Cos[v], (5)/10*Sin[u]*Cos[v], (5)/10*Sin[v]}, {u,
0, 2*Pi}, {v, -Pi/2, Pi/2}};
P2 = {{(5)/10*Cos[u], 0, (5)/10*Sin[u]}, {u, 0, 2*Pi}};
P3 = {{(5)/10*Cos[u], (5)/10*Sin[u], 0}, {u, 0, 2*Pi}};
P4 = {{0, (5)/10*Cos[u], (5)/10*Sin[u]}, {u, 0, 2*Pi}};
U = {P1, P2, P3, P4};
XL = {{-1, 1}, {-1, 1}, {-1, 1}};
XV = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
XS = {"x", "y", "z"};
f[a_, b_, c_] := {a, 1.1*b[[2]]*c};
g[a_, b_] := {(b*# &) /# a};
T = Text ### MapThread[f, {XS, XL, XV}];
A = Line ### MapThread[g, {XL, XV}];
F = ParametricPlot3D[##, Mesh -> False][[1]] & ### U;
OPT = {Boxed -> False, Axes -> False, BoxRatios -> {1, 1, 1},
PlotRange -> XL, ViewPoint -> {2.4, 1.3, 2}};
L = Lighting -> {{"Directional",
RGBColor[0.68, 0.88, 0.96], {{5, 5, 4}, {5, 5, 0}}}};
gr1 = Graphics3D[#, OPT, L] & /# {{Opacity[0.5], F},
{Dashing[{0.03, 0.03}], GrayLevel[0.7], A},
{T}};
Show[gr1]
Here is another take that may be closer to the original. You lose the v7 ability to rotate the graphic with this.
gr1 = Rasterize[Graphics3D[#, OPT, L],
Background -> None] & /# {F, {Dashing[{0.03, 0.03}],
GrayLevel[0.7], A}, T};
Show[gr1]
First one:
ContourPlot[x^2 + (2)*y^2 + (-1)*((1)/(3))*x, {x, -1, 1}, {y, -1, 1},
ContourShading -> False, ContourStyle -> {RGBColor[1, 0, 1]},
Contours -> 20, RegionFunction -> (#1^2 + #2^2 <= 1 &),
BoundaryStyle -> Blue]
[Edit]
Second one, using the given values for A and T:
Show[
ParametricPlot3D[{(5)/10*Cos[u]*Cos[v], (5)/10*Sin[u]*Cos[v], (5)/10*
Sin[v]}, {u, 0, 2*Pi}, {v, -Pi/2, Pi/2},
MeshFunctions -> {#1 &, #2 &, #3 &}, PlotStyle -> Opacity[0.75],
Mesh -> {{0}, {0}, {0}}, MeshStyle -> Black, BoundaryStyle -> Black,
Boxed -> False, Axes -> False, BoxRatios -> {1, 1, 1},
PlotRange -> {{-1, 1}, {-1, 1}, {-1, 1}},
ViewPoint -> {2.4`, 1.3`, 2},
Lighting -> {{"Directional", RGBColor[0.68`, 0.88`, 0.96`],
ImageScaled#{0.1, 0, 1}}}],
Graphics3D[{{Dashing[{0.03, 0.03}], Black, A}, {T}}]
]
I think the axes will need to be done as separate interior/exterior segments.
The great circles show through in this version; preventing that will require drawn partial curves instead of mesh lines, if that's required.