       Re: Vector field with ImplicitPlot ?

• To: mathgroup at smc.vnet.net
• Subject: [mg37417] Re: [mg37377] Vector field with ImplicitPlot ?
• From: Selwyn Hollis <selwynh at earthlink.net>
• Date: Sun, 27 Oct 2002 06:33:18 -0500 (EST)
• References: <200210250648.CAA18194@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```The vector field you want is {D[e[x,v],v], -D[e[x,v],x]}, (or its
negative, depending what direction you want). The following adds this
vector field to your implicit curves.

<<Graphics`ImplicitPlot`;
<<Graphics`PlotField`;

(* example input: *)
V[x_] := x^3 - x;
rect = {{-2, 2}, {-2, 2}};

e[x_, v_] := (1/2)*v^2 + V[x];

t3 = Table[e[x, v] == e1, {e1, 0, 1, 0.2}];

vecfld = {-D[e[x, v], v], D[e[x, v], x]};

{x1, x2} = First[rect];
diag = rect[[2,2]]-rect[[1,1]];
{{xb1, xb2}, {vb1, vb2}} = rect + .05*diag*{{1, -1}, {1, -1}};

curves = ImplicitPlot[Evaluate[t3], {x, x1, x2},
DisplayFunction -> Identity];
vecs = PlotVectorField[vecfld, {x, xb1, xb2}, {v, vb1, vb2},
DisplayFunction -> Identity];
Show[curves, vecs, PlotRange -> rect,
DisplayFunction -> \$DisplayFunction];

---
Selwyn Hollis

> I wish to do plot a vector field plot of an implicit solution.
>
> Equations :
>
> (*V[x] is a polynomial function defined earlier *)
> e[x_, v_] := 1/2 v^2 + V[x];
> t3 = Table[e[x, v] == e1, {e1, 0, 1, 0.2}];
> ImplicitPlot[Evaluate[t3], {x, \(-2\), 2}];
>
> This plots a nice implicit plot for various values of e1. What I wish to do is to attach a
> "sense" to the contours (an arrow that describes the direction of the orbit).
>
> However, I am at a loss as to how to do it with PlotVectorField.
>
> Any help would be appreciated.
>
> PS : Is there a way in which I can "automate" the labelling of the curves with the values
> of e1 they are plotted for (something better than manually editing the labels to the plot
> each time I change the range of e1) ?
>

```

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