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Re: Non-Linear pendulum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104938] Re: Non-Linear pendulum
  • From: dh <dh at metrohm.com>
  • Date: Fri, 13 Nov 2009 05:58:39 -0500 (EST)
  • References: <hdgr31$jbl$1@smc.vnet.net>


Allamarein 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?

> 

Hi Allamarein,

you have to treat the output of NDSolve correctly:



s = \[Theta] /.

    NDSolve[{\[Theta]''[t] == -g/l Sin[\[Theta][t]], \[Theta][0] ==

        Pi/2, \[Theta]'[0] == 0}, \[Theta], {t, 0, 30}][[1]];

Animate[Graphics[Rotate[pendulum, s[t], {0, 0}],

   PlotRange -> {{-2, 2}, {0.5, -2}}], {t, 0, 30},

  AnimationRunning -> True]



Daniel




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