Master of Science

Locked-in planar rotational motion for satellites moving in a gravity gradient field is examined using both analytical and numerical techniques. It is shown that rotational locks at spin rates of n/2 (where n is an integer) satellite rotations per orbit revolution exist for specific combinations of satellite inertia properties and orbital eccentricity. For nearly axial symmetric satellites, the maximum and minimum instantaneous rates which permit the satellite to remain in a particular rotational lock are found analytically by applying the averaging techniques of Kryloff and Bogolinboff and that of Symon. For these cases, it is found that the strength of the higher rotational locks (n > 3) are greater than the strength of the n = 2 or 1/1 rotational lock for proper combinations of lock number, n, and orbital eccentricity. Comparison of the results for the case of the planet Mercury are shown to be in good agreement with both observations of the planet and the 2 numerical calculations of Liu. Numerical results were obtained for representative values throughout the range of satellite inertia properties. Periodic solutions of periods 2π and 4 π are found and their variational stability investigated by Floquet analysis. The results which are presented on stability charts show that for satellites that deviate appreciably from axial symmetry, the stable periodic solutions occur at eccentricities which tend to increase as the absolute value of the lock number |n| increases. Estimates of the strength of these rotational locks are found by applying the phase space technique of Brereton and Modi. For nearly axially symmetric satellites, the results of this technique agreed favorably with the analytical results. Rotational locks for satellites that are not nearly axial symmetric were found in general to be considerably weaker than the more frequently investigated 1/1 lock. / Ph. D.

Command generation is a process by which input commands are constructed or modified such that the system's response adheres to a set of desired performance specifications. Previously, a variety of command generation techniques such as input shaping have been used to reduce residual vibration, limit transient deflection, conserve fuel or adhere to numerous other performance specifications or performance measures. This dissertation addresses key issues regarding the application of command generation techniques to tethered satellite systems. The three primary objectives of this research are as follows: 1) create analytically commands that will limit the deflection of flexible systems 2) combine command generation and feedback control to reduce the retrieval time of tethered satellites, and 3) develop command generation techniques for spinning tether systems. More specifically, the proposed research addresses six specific aspects of command generation for tethered satellites systems: 1) create command shapers that can limit the trajectory tracking for a mass under PD control to a pre-specified limit in real time 2) create commands analytically that can limit the transient deflection of a model with one rigid-body and one flexible mode during rest-to-rest maneuvers 3) command generation for a 2-D model of earth-pointing tethered satellites without tether flexibility, 4) command generation for a 2-D model of earth-pointing tethered satellites to reduce tether retrieval time and reduce swing angle, 5) command generation for a 3-D model of earth-pointing tethered satellites without tether flexibility, and 6) command generation for improved spin-up of spinning tethered satellite systems. The proposed research is anticipated to advance the state-of-the-art in the field of command generation for tethered satellite systems and will potentially yield improvements in a number of practical satellite and tether applications.