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Homework Help: Dumbbell orbit

  1. Mar 28, 2009 #1
    1. The problem statement, all variables and given/known data

    A dumbbell consisting of two spheres of mass [tex]\frac{m}{2}[/tex], and connected by a massless rod of length [tex]2a[/tex] is in circular orbit. The dumbbell is at radius [tex]r_0[/tex] from the planet, and orbits with frequency [tex]\omega_0[/tex]. The angle of the dumbbell to the downward gravitational force is given by [tex]\phi[/tex].

    The position of stable equilibrium for the dumbbell is when [tex]\phi=\pi[/tex], and the position of unstable equilibrium is at [tex]\phi=0[/tex].

    The dumbbell is rocking back and forth. Show that the angular frequency of the rocking motion about the stable equilibrium is equal to [tex]\omega_0*\sqrt{3}[/tex].

    2. Relevant equations

    3. The attempt at a solution

    I keep attempting to set up a lagrangian equation to describe the motion of [tex]\phi[/tex], however, my [tex]\omega_0[/tex] term keeps dropping out at the beginning of my calculations, so I know right there that the answer will turn out wrong.

    What method am I supposed to use?
  2. jcsd
  3. Mar 29, 2009 #2
    Bump. Please please please, this is really important.
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