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Double Pendulum Problem - Lagrangian

  1. Mar 2, 2010 #1
    1. The problem statement, all variables and given/known data

    Rather than solve the double pendulum problem with two masses in the usual way.

    Instead express the coordinates of the second mass, in terms of the coordinates of the mass above it.

    [tex]
    $ x2=x_1+\xi = L_1Sin[\theta]Cos[\phi]+L_2Sin[\alpha]Cos[\beta]$\\
    $ y2=y_1+ \eta = L_1Sin[\theta]Sin[\phi]+L_2Sin[\alpha]Sin[\beta]$\\
    $ z2=z_1-\xi = L_1-L_1Cos[\theta]-L_2Sin[\alpha]Cos[\beta]$
    [/tex]


    Wouldn't you suspect that the Lagrangian remain invariant? Is there a way to reparameterize these equations?

    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Mar 7, 2010 #2
    Re: Pendulum

    No one has any opinions?

    Does anyone know what I'm talking about?
     

    Attached Files:

    Last edited: Mar 7, 2010
  4. Mar 7, 2010 #3
    Re: Pendulum

    Then the problem I'm interested in is the following
     

    Attached Files:

  5. Mar 9, 2010 #4

    Attached Files:

    Last edited: Mar 9, 2010
  6. Mar 9, 2010 #5
    Re: Pendulum

    I'm not sure if I had defined z_2 correct:
    [tex]


    $ z2=z_1-\xi = L_1-L_1Cos[\theta]-L_2Cos[\alpha]$

    [/tex]
     
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