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Double pendulum, time question

  1. Mar 9, 2010 #1

    fluidistic

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    Gold Member

    I'm probably going to learn about the double pendulum in a few weeks, however I have a question that I can't get rid off from my head.
    Is there a time (I imagine it to be very large) where the pendulum reach the initial position/configuration? In another words, a time where it moves as it has moved. Maybe we can call this a period, but I'm not really sure.
    If I remember well, Poincaré's recurrence theorem implies the existence of such a time.

    Mathematically I must have the motion equation under my eyes and set [tex]t=0[/tex]. I do the same but setting [tex]t=t_1[/tex]. And lastly I equal both equation and I solve for [tex]t_1[/tex]. I'm guessing it's very hard to solve for [tex]t_1[/tex] since I never heard of a period of a double pendulum.
    Do someone has something to say?
     
  2. jcsd
  3. Mar 10, 2010 #2

    Dale

    Staff: Mentor

    In general, no. A double pendulum is a chaotic system and will not generally return to the same configuration as before. Also, you can usually only solve the equations of motion numerically and they are numerically unstable over long periods of time.
     
  4. Mar 10, 2010 #3

    fluidistic

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    Gold Member

    Ok thanks a lot for the information.
     
  5. Mar 22, 2010 #4
    A double pendulum executes simple harmonic motion (two normal modes) when displacements from equilibrium are small. However, when large displacements are imposed, the non-linear system becomes dramatically chaotic in its motion and demonstrates that deterministic systems are not necessarily predictable.

    http://www.fas.harvard.edu/~scdiroff/lds/MathamaticalTopics/ChaoticPendulum/ChaoticPendulum002.gif
    ________________
    http://makersmarket.com/products/91-chaotic-pendulum [Broken]
     
    Last edited by a moderator: May 4, 2017
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