Results 1 to 2 of 2

Math Help - Double Pendulum Nightmare

  1. #1
    Newbie
    Joined
    Aug 2008
    Posts
    11

    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  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Aug 2008
    Posts
    903
    I'd write:

    y=\dot{\phi_1}

    z=\dot{\phi_2}

    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

    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 k's and then solve it numerically for y,z,\phi_1,\phi_2: it's cake using Mathematica's \text{NDSolve} (I think).
    Last edited by shawsend; September 17th 2008 at 05:35 AM. Reason: corrected formulas
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Perms and Combs... a nightmare!
    Posted in the Statistics Forum
    Replies: 4
    Last Post: November 9th 2011, 07:09 AM
  2. Solving double pendulum with runge kutta
    Posted in the Math Software Forum
    Replies: 0
    Last Post: January 5th 2011, 10:34 PM
  3. A statistical nightmare
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: September 16th 2009, 06:50 PM
  4. Integrals Nightmare
    Posted in the Calculus Forum
    Replies: 10
    Last Post: October 16th 2008, 09:01 AM
  5. nightmare integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 19th 2008, 06:05 PM

Search Tags


/mathhelpforum @mathhelpforum