Oscillating satellites about the straight line equilibrium points.
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Clayton, Robert Lee
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The problem as studied in this thesis is the behavior of a satellite at the three equilibrium points. When a satellite is displaced from rest at one of these points it will either oscillate or rapidly leave the system. The equations of motion were first set up between the satellite and two other rotating bodies. These equations were then expanded in series and certain restrictions placed upon them. With these restrictions, constants of integration were found, and the integrated equations of motion were also found. An application was then made to the Solar System in which the Sun and Jupiter were taken as the major bodies. The masses of these two bodies were then substituted into the equations of motion and equations were found for the three points of equilibrium. The orbits were then plotted at the three points.