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Homework Help: Find Lagrangian and Hamaltonian equations of motion in polar coord.

  1. Sep 22, 2008 #1
    1. The problem statement, all variables and given/known data

    A particle of mass m is attracted to a force center with the force center with the force of magnitude k/r2 . Use plane polar coordinates and find Hamilton’s equations of motion.

    2. Relevant equations

    (L)agrangian = T-U , U=-[tex]\int[/tex]F dr

    3. The attempt at a solution

    I can get the Hamiltonian equations of motion but what I am not confident about is the equations for kinetic and potential energy.
    Are they correct?
    Did I obtain the potential energy equation correctly?

    Any input would be appreciated. Thank you.

    http://b.imagehost.org/0511/tmp37F.jpg [Broken]
     
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Sep 22, 2008 #2

    gabbagabbahey

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    Homework Helper
    Gold Member

    The problem tells you to use plane polar coordinates; which means it is a 2D problem and so there are two coordinates and conjugate momentums to consider. Why haven't you included any [tex]\phi [/tex] and [tex] p_{\phi} [/tex] terms in your Hamiltonian?
     
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