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>*Reply-to*: murray at math.umass.edu

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

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