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Homework Help: The elastic ribbon sine-Gordon model

  1. Nov 17, 2007 #1
    Hello,
    I'd like to verify that the elastic ribbon model [ depicted here: http://www.math.h.kyoto-u.ac.jp/~takasaki/soliton-lab/gallery/solitons/sg-e.html ] is governed by the sine-Gordon equation. I suppose this can be shown by writing the lagrangian [itex]L = T - V[/itex] and looking at the variation. The kinetic energy for a single single pendulum is [itex]T =\tfrac{1}{2} \dot{\phi}^2 [/itex], but how can i describe potential [itex]V[/itex] now that each pendulum is coupled to its neighbours?

    All the best
    SF
     
    Last edited: Nov 17, 2007
  2. jcsd
  3. Nov 17, 2007 #2
    According to Wikipedia the the s-G equation is the Euler-Lagrange equation of the following lagrangian
    [tex] \mathcal{L}(\phi) = \frac{1}{2}(\phi_t^2 - \phi_x^2) + \cos\phi. [/tex]
    Thus i suppose my question is simply how to derive this lagrangian for the mentioned mechanical system.
     
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