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Lagrangian question, inverted pendulum (Very near to the answer!)

  1. May 27, 2013 #1
    1. The problem statement, all variables and given/known data

    Consider the setup shown in the gure below. The cart of mass M moves along
    the (horizontal) x axis. A second mass m is suspended at the end of a rigid, massless
    rod of length L. The rod is attached to the cart at point A, and is free to pivot about A in the x-y plane. Frictional forces may be ignored.

    72evc1.jpg

    2. Relevant equations

    I got the same lagrangian as in wikipedia, so i think it's right.
    http://en.wikipedia.org/wiki/Inverted_pendulum



    3. The attempt at a solution

    abvekBMO.jpg
     
  2. jcsd
  3. May 27, 2013 #2
    Your Lagrangian and equations of motions are correct. I'm pretty sure A1 has to be zero so that your solution does not blow up at infinity. Then you can use the initial conditions given in the problem to solve for A2 and A
     
  4. May 28, 2013 #3
    I know right? But I can't find any mathematical reason why A1 = 0...I get 2 values of β in the characteristic equation where α = A*exp(βt)..
     
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