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 Madhusudan Singh wrote: > 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) ? >

**References**:**Vector field with ImplicitPlot ?***From:*Madhusudan Singh <spammers-go-here@yahoo.com>