Re: Non-Linear pendulum

*To*: mathgroup at smc.vnet.net*Subject*: [mg104925] Re: Non-Linear pendulum*From*: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>*Date*: Fri, 13 Nov 2009 05:56:11 -0500 (EST)*References*: <hdgr31$jbl$1@smc.vnet.net>

Several errors here. 1) You use the undefined theta instead of the solution of the equation (s). 2) The result in s should be morphed a bit to be useable 3) Rotate should not be used in a graphics environment. Use GeometricTransformation and RotationTransform instead. 4 Spelling of \[Theta] as \[Theta[ doesn't help either. The following works: pendulum = {Line[{{0, 0}, {0, -1}}], Circle[{0, -1.3}, 0.3]}; l = 20; g = 9.81; s = \[Theta] /. (NDSolve[{\[Theta]''[ t] == -g/l Sin[\[Theta][t]], \[Theta][0] == Pi/2, \[Theta]'[0] == 0}, \[Theta], {t, 0, 30}])[[1, 1]] Animate[Graphics[ GeometricTransformation[pendulum, RotationTransform[s[t]]], PlotRange -> {{-2, 2}, {0, -2}}], {t, 0, 30}, AnimationRunning -> False] Cheers -- Sjoerd On Nov 12, 1:21 pm, Allamarein <matteo.diplom... at gmail.com> wrote: > I'm getting to know Mathematica. I want to compile a code to see the > non-linear pendulum behavior. > > pendulum= {Line[{{0, 0}, {0, -1}}], Circle[{0, -1.3}, 0.3]}; > l = 20; > g = 9.81; > s = NDSolve[ > { \[Theta]''[t] == -g /l Sin[\[Theta][t]], > \[Theta][0] == Pi/2, > \[Theta]'[0] == 0}, \[Theta], > {t, 0, 30}]; > Animate[ > Graphics[Rotate[pendulum, \[Theta[]t], {0, 0}], > PlotRange -> {{-2, 2}, {0, -2}}], > {t, 0, 30}, AnimationRunning -> False] > > This code doesn't work. I realized my error is in Rotate argument. If > I change this line with: > > Graphics[Rotate[pendulum, Sin[t], {0, 0}] > > code runs, but it's not the result (obviously). > How can I correct my code, to see the pendulum oscillates with \[Theta] > [t] law?