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Solve problem without Lagrange Equations.

  1. Jul 20, 2011 #1
    A friend and I were debating the solution to this problem, seen below, and cannot solve it without using Lagrange equations but it is suppose to have a solution that is super simple; but we didn't see it.

    Anyway, it is a old qualifier question from the Univ. of Wisconsin (open record so anyone can view it). NOTE: This is NOT a homework question NOR will it appear on another qualifier. My friend and I were simply arguing this:

    1. The problem statement, all variables and given/known data

    Suppose the US and Russia were to jointly build a space station with two identical spherical modules (mass, m) to house their crews, and that they are joined by an effectively mass-less conduit (length, d) for astronauts to visit each other. What is the stable orientation of this satellite? (i.e., determine the angle α between the conduit and the line joining the c.m of the satellite and the Earth’s center). Hint: The potential energy of a non-spherical satellite varies slightly, depending on its orientation relative to its orbit.


    2. Relevant equations
    Using general Newtonian Mechanics.


    3. The attempt at a solution
    The solution we got was very lengthy using Lagrange Equations of motion, we are interested in how anyone could do this a "quick way". Note: We both haven't touched classical mechanics in a long time.
     
  2. jcsd
  3. Jul 20, 2011 #2

    berkeman

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    Staff: Mentor

    Can you calculate the potential energy of the satellite for horizontal and vertical orientations? What are they?
     
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