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Wondering
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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:
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.
Using general Newtonian Mechanics.
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.
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:
Homework Statement
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.
Homework Equations
Using general Newtonian Mechanics.
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.