Equations of Motion of a Passive Satellite Stabilization System.

by Richard H. Frick

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A formulation of equations of motion of a passive satellite stabilization system consisting of a satellite with an extendable boom deploying a spring and end-mass. This configuration is in equilibrium if the boom, spring, and end-mass are aligned along the vertical either above or below the main satellite body. Oscillations about the equilibrium position are damped by mechanical hysteresis in the spring and magnetic hysteresis in sets of permeable rods connected to the body. The analysis treats the system as a coupled, seven-degree-of-freedom configuration, including three degrees of rotational freedom of the satellite-boom combination, three degrees of translational freedom of the end-mass, and one degree of rotational freedom of the end-mass about its axis of symmetry. The resulting equations are not restricted to small angular deviations from equilibrium and do not require that the vehicle be on a circular orbit. In addition, the analysis allows for external disturbances. 69 pp

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