Satellite relative motion propagation and control in the presence of J2 perturbations

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Title: Satellite relative motion propagation and control in the presence of J2 perturbations
Author: Sengupta, Prasenjit
Abstract: Formation flying is a new satellite mission concept that is concerned with clusters of satellites in neighboring orbits cooperating to perform a specific task . The tasks may be Earth observation or space -based interferometry where a cluster of small satellites is able to fulfill the same requirements as that of a larger , monolithic satellite . There exist a variety of models for the study of relative motion between two satellites . These include models based upon differential orbital elements , and relative position and velocity coordinates . Extensive work has been done on such models , both in the absence and presence of the J2 perturbation arising from the aspherical nature of the Earth , which causes variations in the orbital elements that describe the orbit . The approximate relative motion can be obtained analytically by using mean elements . However , the true orbit can only be described by the instantaneous osculating elements . An analytical method to propagate the relative motion between two satellites in highly elliptic orbits is the main focus of this thesis . The method is kinematically exact and it maintains a high degree of accuracy even in the presence of J2 perturbations . Mean orbital elements are used for orbit propagation , and expansions involving the powers of eccentricity are not utilized . The true anomaly of the reference satellite is treated as the independent variable , instead of time . The relative orbit kinematics are obtained by using a projection onto a unit sphere . This procedure allows the relative position variables to be treated as angles depending on the orbital element differences . The effect of adding short -period corrections due to J2 to the mean elements is also studied . Finally , the problem of formation reconfiguration is studied . The reconfiguration of a formation may be achieved by using impulsive thrust (velocity increments ) or continuous control . This thesis presents a method to obtain the optimal velocity increments through numerical optimization , utilizing the analytical technique developed for relative orbit propagation . A continuous control law is also developed using a candidate Lyapunov function , and the asymptotic stability of the closed -loop system is ascertained .
URI: http : / /hdl .handle .net /1969 .1 /518
Date: 2004-09-30

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Satellite relative motion propagation and control in the presence of J2 perturbations. Available electronically from http : / /hdl .handle .net /1969 .1 /518 .

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