Re: Varying a constant in an ODE to Manipulate solution

*To*: mathgroup at smc.vnet.net*Subject*: [mg126907] Re: Varying a constant in an ODE to Manipulate solution*From*: Narasimham <mathma18 at hotmail.com>*Date*: Sun, 17 Jun 2012 03:56:16 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201206130857.EAA03730@smc.vnet.net> <jreout$nqu$1@smc.vnet.net>

On Jun 15, 12:41 pm, Murray Eisenberg <mur... at math.umass.edu> wrote: > It's not clear to me what you want to do. I hope this reply clarifies, and my broader question too. > Do you want to create 3D-parametric plot of the trajectory in space -- > possibly as a dynamic with the time t as dynamic parameter? Yes. I can get this plot OK simply as: Manipulate[ParametricPlot3D[Evaluate[sol[c][[1]]], {t, -3, 3}, PlotStyle -> {Red, Thick}, AspectRatio -> Automatic, PlotRange -> {{-3, 3}, {-10, 10}}], {c, -0.5, 2, 0.2}] Also I have asked in a separate but related question now under clearance by moderators regarding Clairaut's Equation_ How to include traces of these lines in the plot and not have them flying in the 3space on the Manipulate command. Call them t parameter lines as t is continuous and c is discrete. > And/or do one of those same things but do it just in 2D, selecting some > pair of the 3 components of the solution function? Yes, that was my query. Bob Hanlon pointed out my error. (Evaluating together was needed). > Or a 3D-parametric plot of the trajectory over a fixed-duration time in= terval, but dynamic > with c as control variable? Yes, in fact that is going to be my next question now, and thanks that you have foreseen it ! Call these lines c parameter lines as c would be the continuous control variable and t's would be discrete. In this case, each time dot is extruded or curvilinearly dragged across the surface, cutting the t lines. Bringing together action of control variables t and c, we have a surface sol[c_,t_] which can be computed and plotted. t and c are two parameters for this patch. How can this be done? I am almost sure this is doable. I shall try for Clairaut's 2D problem and send result when done. Regards Narasimham > On 6/13/12 4:57 AM, Narasimham wrote: > > Same topic is continued. Thanks to Murray Eisenberg and Bob Hanlon > > > All variables or a single variable are easily pocked out from sol[c_] > > list for plotting. > > But how to pick out two out of them for ParametricPlot ( 2D) ? > > > sol[c_] := {x[t], y[t], z[t]} /. > > First[NDSolve[{y''[t] + Sin[y[t]/c] == 0, y'[0] == 0, > > y[0] == 1/(1 + c), x'[t] == t, x[0] == c^2, > > z'[t] == 2 c x[t] - y[t], z[0] == 2}, {x, y, z}, {t= , -3, 3}]] > > Manipulate[ > > Plot[Evaluate[sol[c]], {t, -3, 3}, PlotStyle -> {Red, Thick}, > > AspectRatio -> Automatic, > > PlotRange -> {{-3, 3}, {-10, 10}}], {c, -0.5, 2, 0.2}] > > Manipulate[ > > Plot[Evaluate[sol[c][[1]]], {t, -3, 3}, PlotStyle -> {Red, Thick= }, > > AspectRatio -> Automatic, > > PlotRange -> {{-3, 3}, {-10, 10}}], {c, -0.5, 2, 0.2}] > > " 2 parameter Dynamic manipulation not OK" > > Manipulate[ > > Plot[{Evaluate[sol[c][[1]]], Evaluate[sol[c][[1]]]}, {t, -3, 3}, > > PlotStyle -> {Green, Thick}, AspectRatio -> Automatic, > > PlotRange -> {{-3, 3}, {-10, 10}}], {c, -0.5, 2, 0.2}] > > -- > Murray Eisenberg murrayeisenb...@= gmail.com > 80 Fearing Street phone 413 549-10= 20 (H) > Amherst, MA 01002-1912

**References**:**Varying a constant in an ODE to Manipulate solution***From:*Narasimham <mathma18@hotmail.com>