Physics
Scientific paper
Sep 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992phdt........64h&link_type=abstract
Ph.D. Thesis Princeton Univ., NJ.
Physics
Electric Propulsion, Elliptical Orbits, Orbital Mechanics, Spacecraft Orbits, Trajectory Optimization, Transfer Orbits, Eccentricity, Optimal Control, Spacecraft Trajectories
Scientific paper
Researchers have studied transfers for spacecraft using electric propulsion systems for many years. Previous work can be put into two categories--approximate results for restricted cases and numerical optimization results for specific missions or simple geometries. Approximate results exist for two limiting cases: many-revolution transfers with slowly changing orbit elements for which averaging applies and short duration transfers with small changes in the orbit elements for which linearization applies. Mission results are limited to transfers between circular orbits, as for the earth-Mars and earth-Venus missions, and escape problems. This research focuses on (1) the development of a systematic and accurate procedure for solving minimum-fuel, power limited transfers, and (2) the application of this procedure to characterize multiple revolution, minimum-fuel, power-limited transfers. The solution procedure is based on averaging. The adjoint from the average solution, referred to as the average adjoint, is the basis for two approximate solutions. In the first approximate solution the initial average adjoint serves as an estimate of the unknown initial adjoint. In the second approximation, the average adjoint is substituted into the minimum-fuel control law to provide an approximate optimal control. A canonical transformation is developed to transform the average adjoint from orbit element coordinates, which are used for averaging, to trajectory variable coordinates, which are used for numerical integration. These approximations are accurate for multiple revolution transfers. Their accuracy is inversely proportional to the transfer time, and transfers with extremely low or extremely high eccentricity are less accurate than those with moderate eccentricity for a given transfer time. The transformed adjoint from the average solution is used to generate the locally minimizing trajectories that are used in the characterization. Illustrative transfers are presented for many transfer times and transfer geometries. This characterization finds that (1) averaging qualitatively predicts the secular behavior of the semimajor axis and quantitatively predicts the eccentricity and argument of periapse for transfers with at least three revolutions; and (2) the linear theory qualitatively predicts the thrust magnitude and direction for an individual revolution given the secular predictions in the orbit elements.
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