Rewrite a Manipulate to call NDSolve just once?

*To*: mathgroup at smc.vnet.net*Subject*: [mg127149] Rewrite a Manipulate to call NDSolve just once?*From*: RBaillie <bobbaillie at frii.com>*Date*: Mon, 2 Jul 2012 05:29:27 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Here is a nice pendulum demo from http://demonstrations.wolfram.com/NonlinearizedMotionOfASimplePendulum Like all other demos I've seen, NDSolve[ ] is called many times. Is there a way to write this so that NDSolve is called once each time the "release system" button is pressed? Manipulate[ If[run == time, run = 0]; Module[ { sol, \[Theta], t }, sol = NDSolve[{ \[Theta]''[t] + (9.8/l)*Sin[\[Theta][t]] == 0, \[Theta][0] == theta, \[Theta]'[0] == thetaPrime }, \[Theta], {t, 0, time}, Method -> "StiffnessSwitching"]; With[{angle = \[Theta][run] /. First[sol]}, Graphics[ { {Lighter[Brown], Rectangle[{-4, 0}, {4, .5}]}, (* top bar *) {Darker[Red], Disk[{0, 0}, .1]}, (* top pivot *) {Line[{{0, 0}, {l*Sin[angle], -l*Cos[angle]}}]}, (* pendulum *) {Blue, Disk[{l*Sin[angle], -l*Cos[angle]}, .2]} (* mass at bottom *) } , PlotRange -> {{-4, 4}, {.5, -4}}, ImageSize -> {500, 300} / 2 ] (* end Graphics *) ] (* end With *) ] (* end Module *) , { {l, 3, "length of pendulum"}, .5, 3.5, .1, Appearance -> "Labeled"}, { {theta, Pi/4, "initial angle (radians)"}, 0, Pi/2, .01, Appearance -> "Labeled"}, { {thetaPrime, 0, "initial angular velocity"}, 0, 5, Appearance -> "Labeled"}, { {time, 10.00, "time to watch motion"}, 0, 20, .01, Appearance -> "Labeled"}, { {run, 0, "release system"}, 0, time, .001, ControlType -> Trigger, AnimationRate -> 1}, SynchronousUpdating -> False, AutorunSequencing -> {1, 2} ]