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Thread: Double Pendulum Nightmare

  1. #1
    Aug 2008

    Question Double Pendulum Nightmare

    Hi all >> see attached images of pendulum and 2nd order model

    Currently working on a problem, creating a model for a double pendulum system, we have been given the initial non-linear system of 2x 2nd order equations which have to simplified to 4x 1st order non linear equations; I know the basic theory and know that I can simplify the equations by compacting the variables and going from there

    ie. representing them as,

    aO1'' + bO2'' + c = 0
    dO1'' + eO2'' + f =0

    when O1'' = 2nd derivative of phi/ angular acceleration

    just a bit lost in how to reproduce the final equations?

    The equations are crazy but the theory should be basically the same, would appreciate any ideas......
    Attached Thumbnails Attached Thumbnails Double Pendulum Nightmare-system.jpg   Double Pendulum Nightmare-equations.jpg  
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  2. #2
    Super Member
    Aug 2008
    I'd write:

    $\displaystyle y=\dot{\phi_1}$

    $\displaystyle z=\dot{\phi_2}$

    $\displaystyle k_1y'+k_2\cos(\phi_1-\phi_2)z'+k_2\sin(\phi_1-\phi_2)z^2+k_3\frac{g}{l}\sin(\phi_1)=0$

    $\displaystyle k_2\cos(\phi_1-\phi_2)y'+k_5 z'-k_2\sin(\phi_1-\phi_2)y^2+k_2 g\sin(\phi_2)=0$

    may want to double check that. Then assign all the $\displaystyle k's$ and then solve it numerically for $\displaystyle y,z,\phi_1,\phi_2$: it's cake using Mathematica's $\displaystyle \text{NDSolve}$ (I think).
    Last edited by shawsend; Sep 17th 2008 at 05:35 AM. Reason: corrected formulas
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