Dynamics and control of satellite relative motion in a central gravitational field

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Title: Dynamics and control of satellite relative motion in a central gravitational field
Author: Sengupta, Prasenjit
Abstract: The study of satellite relative motion has been of great historic interest , primarily due to its application to rendezvous , intercept , and docking maneuvers , between spacecraft in orbit about gravitational bodies , such as the Earth . Recent interest in the problem of satellite formation flight has also led to renewed effort in understanding the dynamics of relative motion . Satellite formations have been proposed for various tasks , such as deep -space interferometry , and terrestrial observation , among others . Oftentimes , the rich natural dynamics of the relative motion problem near a gravitational body are exploited to design formations of a specific geometry . Traditional analysis models relative motion under the assumptions of a circular reference orbit , linearized differential gravity field (small relative distance ) , and without environmental perturbations such as oblateness effects of the attracting body , and atmospheric drag . In this dissertation , the dynamics of the relative motion problem are studied when these assumptions are relaxed collectively . Consequently , the combined effects of nonlinearity , eccentricity , and Earth oblateness effects on relative motion , are studied . To this end , coupling effects between the various environmental perturbations are also accounted for . Five key problems are addressed - the development of a state transition matrix that accounts for eccentricity , nonlinearity , and oblateness effects ; oblateness effects on averaged relative motion ; eccentricity effects on formation design and planning ; new analytical expressions for periodic relative motion that account for nonlinearity and eccentricity effects ; and a solution to the optimal rendezvous problem near an eccentric orbit . The most notable feature of this dissertation , is that the solutions to the stated problems are completely analytical , and closed -form in nature . Use has been made of a generalized reversion of vector series , and several integral forms of Kepler ? ? ? ? ? ?s equations , without any assumptions on the magnitude of the eccentricity of the reference orbit .
URI: http : / /hdl .handle .net /1969 .1 /4724
Date: 2007-04-25

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Dynamics and control of satellite relative motion in a central gravitational field. Available electronically from http : / /hdl .handle .net /1969 .1 /4724 .

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