       Re: Varying a constant in an ODE to Manipulate solution

• To: mathgroup at smc.vnet.net
• Subject: [mg126877] Re: Varying a constant in an ODE to Manipulate solution
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Fri, 15 Jun 2012 03:40:21 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201206130857.EAA03730@smc.vnet.net>

```It's not clear to me what you want to do. Do you want to create
3D-parametric plot of the trajectory in space -- possibly as a dynamic
with the time t as dynamic parameter?  Or a 3D-parametric plot of the
trajectory over a fixed-duration time interval, but dynamic with c as
control variable?

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?

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,
>       y == 1/(1 + c), x'[t] == t, x == c^2,
>       z'[t] == 2 c x[t] - y[t], z == 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][]], {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][]], Evaluate[sol[c][]]}, {t, -3, 3},
>    PlotStyle ->  {Green, Thick}, AspectRatio ->  Automatic,
>    PlotRange ->  {{-3, 3}, {-10, 10}}], {c, -0.5, 2, 0.2}]

--
Murray Eisenberg                     murrayeisenberg at gmail.com
80 Fearing Street                    phone 413 549-1020 (H)
Amherst, MA 01002-1912

```

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