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MathGroup Archive 2007

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Re: Foucault pendulum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80206] Re: Foucault pendulum
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Tue, 14 Aug 2007 07:20:01 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <f9mq8f$r63$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de

Hi,

something like this:

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]};

Block[{\[Omega] = 1, \[CapitalOmega] = 1/16, \[Phi] = Pi/6},
  sol = NDSolve[
    Join[fde, {x[0] == 1, y[0] == 1, x'[0] == 0, y'[0] == 0}],
    {x[t], y[t]}, {t, 0, 64 Pi}]
  ]

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

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

Manipulate[
  DynamicModule[{traj},
   traj = ParametricPlot3D[
     pendelPos[{x[t], y[t]} ] /. sol[[1]], {t, t1, t1 + 4 Pi}
     ];
   Graphics3D[
    {traj[[1]], pendel[t1]}, PlotRange -> {{-2, 2}, {-2, 2}, {-4, 0}}
    ]], {t1, 0, 60 Pi}
  ]

Regards
   Jens

dimitris wrote:
> Hello.
> Does anyone have notebooks
> demonstrating Foucault's pendulum?
> 
> Thanks
> Dimitris
> 
> 


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