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Landau/Lifshitz problem, comment on the result?

  1. Oct 2, 2011 #1
    So I was debating whether or not to post this in the homework session but I feel the question I'm asking belongs here.

    I just worked out a problem for my Classical Mechanics Assignment and while I arrived at the solution I am wonder what 'comment' can be made about the result.

    It is from L/L Mechanics, page 12 problem 4.

    It asks you to find the Lagrangian for a system that looks like the picture attached that is rotating at a constant angular velocity Omega around the fixed vertical axis.

    The Lagrangian comes out to be:

    [tex] L = m_{1}a^{2}(\dot{\theta}^{2} + \sin^{2}(\theta)\Omega^{2}) + 2m_{2}a^{2}\sin^{2}(\theta)\dot{\theta}^{2} + 2(m_{1} + m_{2})gacos(\theta) [/tex]

    I guess my real question is HOW can you recognize how the system will behave just by looking at the Lagrangian. I realize I could solve the Euler-Lagrange equations and solve for the equation of motion in terms of theta but that isn't what this is asking. I feel like there should be some intuitive description of the system just by looking at the Lagrangian.

    Any thoughts?
     

    Attached Files:

  2. jcsd
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