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MathGroup Archive 2007

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Re: Foucault pendulum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80147] Re: Foucault pendulum
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Tue, 14 Aug 2007 06:49:19 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <f9mq8f$r63$1@smc.vnet.net> <f9p4db$qdh$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de

Hi,

sorry the last version has a bug
here is a nicer version

pendelPos[{x_, y_}] := {x, y, -Sqrt[10 - x^2 - y^2]}

pendel[tau_?NumericQ,
   sol_] := ({AbsoluteThickness[3],
      Line[{{0, 0, 0}, pendelPos[{x[t], y[t]}]}],
      Sphere[pendelPos[{x[t], y[t]}], 0.15]} /. sol[[1]]) /. t -> tau

Manipulate[
  DynamicModule[{traj, sol, fed, fulltraj},
   fde =
    {x''[t] == -\[Omega]^2*x[t] +
       2 \[CapitalOmega]*Sin[\[Phi]]*y'[t] ,
     y''[t] == -\[Omega]^2*y[t] -
       2 \[CapitalOmega]*Sin[\[Phi]]*x'[t]};
   sol = NDSolve[
     Join[fde, {x[0] == 2, y[0] == 2, x'[0] == 0, y'[0] == 0}],
     {x[t], y[t]}, {t, 0, 64 Pi}, MaxSteps -> Infinity];
   fulltraj = ParametricPlot3D[
     {x[t], y[t], -4} /. sol[[1]], {t, 0, 64 Pi},
     PlotPoints -> 1024
     ];
   traj = ParametricPlot3D[
     pendelPos[{x[t], y[t]} /. sol[[1]]], {t, t1, t1 + 4 Pi},
     PlotStyle -> RGBColor[1, 0, 0]
     ];
   Graphics3D[
    {traj[[1]], fulltraj[[1]], pendel[t1, sol]},
    PlotRange -> {{-2.5, 2.5}, {-2.5, 2.5}, {-4, 0}}
    ]], {{\[Omega], 1, "Pendel Frequence"}, 0.1,
   10}, {{\[CapitalOmega], 1/16, "Earth Circum Frequence"}, 0,
   1/2}, {{\[Phi], Pi/3, "Latitude"}, 0, Pi/2}, {{t1, 0, "time"}, 0,
   60 Pi}
  ]

Regards
   Jens

dimitris wrote:
> On 12    , 14:17, dimitris <dimmec... at yahoo.com> wrote:
>> Hello.
>> Does anyone have notebooks
>> demonstrating Foucault's pendulum?
>>
>> Thanks
>> Dimitris
> 
> I mean the motion of a Foucalt's pendulum of course.
> 
> Dimitris
> 
> 


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