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Double pendulum - solving with energy and Simulink

  1. Jan 2, 2015 #1
    Hi everyone,

    I am trying to familiarize myself with Simulink by graphically drawing out differential equations, but ran into a snag with a double pendulum on a cart. Anyways, I neglect friction or other damping effects and say that

    NfjXqjv.png

    From there I simply just sum the energies, which ends up as:

    BA9AeIJ.png

    And then differentiating with respect to time ends up with:

    OpX823N.png

    This seemed fine to me, and I started creating my Simulink model. The way that works is I have a loop with each variable connecting to each other in a certain way (i.e. xddot = stuff, thetaddot = other stuff). The issue is, when solving for any of the second order derivatives it is necessary to divide by the first order derivative. For example, to solve for the acceleration of x it is necessary to divide by the velocity of x. What if the velocity happens to be zero? In that case my Simulink model fails.

    I did it with energy because it seemed a lot easier. Is there any other way to isolate the variables without dividing by terms like velocity which could be zero?
     
  2. jcsd
  3. Jan 7, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
  4. Jan 16, 2015 #3
    It might be easier to form the Lagrangian and just use the Euler-Lagrange equations and put those differential equations in Simulink. I've done some Simulink models for control systems of inverted pendulums and haven't had any problems separating out the double derivatives in matrix form.

    This link contains all the derivations, so hopefully you can just plug it in and get something:
    http://scienceworld.wolfram.com/physics/DoublePendulum.html

    Hope that helps!
     
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