UBC Theses and Dissertations
Effect of environmental forces on the attitude dynamics of gravity oriented satellites Flanagan, Ralph Clarence
The influence of the major environmental forces on the attitude response of gravity gradient satellites is investigated using analytical and numerical techniques. The study establishes not only the effect of these forces on system performance but also their relative importance. The problem is investigated in the order of increasing difficulty which corresponds to a systematic reduction in altitude. In general, the non-linear, non-autonomous nature of the system renders the determination of a closed form solution virtually impossible. Hence, numerical techniques are employed, in conjunction with invariant surfaces or integral manifolds, to analyse the system. For a given set of parameters, the largest such surface defines the bound of stable motion; on the other hand, the smallest surface that can be found (i.e., a line or set of lines) represents the dominant periodic solution with which these manifolds are associated. The analysis establishes the importance of periodic solutions as they provide the 'frame' about which stability charts are built. Furthermore, a variational stability analysis of these solutions, using Floquet theory, accurately determines the termination of the spikes and establishes the critical eccentricity for stable motion. Phase I investigates the attitude dynamics of satellites at high altitudes where gravity gradient and direct solar radiation constitute the predominant torques. The approximate closed form solution, obtained using the WKBJ and Harmonic Balance methods, was found to predict the librational response of a satellite with considerable accuracy. As the satellites requiring station keeping permit only small amplitude motion, the analytical results are of sufficient accuracy to be useful during preliminary design stages. The response and stability bounds of the system, obtained numerically, are shown through the use of 'system plots' and 'stability charts'. The results indicate a considerable effect due to solar radiation on the attitude dynamics of a satellite. The use of solar radiation in controlling the satellite attitude is explored. The optimized results show this system to be quite effective, being capable of providing a pointing accuracy of 0-5° depending on orbit eccentricity. The extension of the analysis to the intermediate altitude ranges, where direct earth radiation, its albedo and shadow become significant, is undertaken in phase II. A comprehensive investigation was made possible by the determination of closed form expressions for earth radiation forces. This was accomplished through the concept of cutting plane distance ratios. The analysis shows only local variations due to earth radiations without substantially affecting the maximum librational amplitude or mainland stability area. Hence, for all practical purposes, direct earth radiation, its albedo and shadow can be neglected in such studies. Phase III investigates the dynamics of close earth satellites in the presence of aerodynamic and radiation forces, thus covering the remaining altitude range. The results show that a precise dynamic analysis requires the consideration of both aerodynamic and direct solar radiation forces. The investigation helps in establishing an altitude range in which a pure gravity gradient analysis is likely to be most applicable. The application of this analysis to the representative gravity gradient satellite, GEOS-A, over the entire altitude range, exemplifies the findings of the parametric study.
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