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Euler angles and symmetric top

  1. Nov 4, 2008 #1
    1. The problem statement, all variables and given/known data
    Check out problem 5.7 part a

    I want to express the exterior gravitational potential in terms of the Euler angles so that I might eventually use (dV/dB)B=B0 = 0 - the condition for equilibrium.

    I am therefore expecting the Lagrangian to be cyclic in terms of the other two angles.

    2. Relevant equations
    The symmetric top equations in terms of the Euler angles.

    3. The attempt at a solution
    I take one of the axes in the rotated frame (e3) to be along the axis of rotation to be earth and describe the colatitude angle wrt to that axis.

    My first problem is how to resolve the vector over the non-orthogonal vectors. I have made a few attempts but until I take the azimuthal angle (and thus add another variable to the problem) I cant do that. I did take the assumption that the azimuthal angle is 0 so that the position vector is right above one of the axis. (I dont know whether its correct or not).

    My second problem is that no matter what I do, I cant get rid of the r^-1 and r^-2 which appear in the gravitational potential.
  2. jcsd
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