Dynamical system theory application to earth- satellite pitch attitude librations

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We have developed in this thesis, an analytical methodology for solving a differential equation model representing Pitch Attitude librations of an Earth —Satellite. This highly non linear equation of motion of the Pitch Attitude librations is transformed into a system of equations in terms of the anomaly. The system of equations is linearized about the origin and then analyzed in the context of Dynamical System Theory for its equilibrium configuration and periodicity. We obtain the non linear system by augmenting the level of non linearity of the linearized system through the addition of non linear terms. In our analytical approach, first, the linearized system is solved using the Floquet theory which is based on the periodicity of the coefficient matrix. Then, the complete non linear solution is obtained by a successive approximation scheme involving the fundamental matrix. This methodology is used to analyze our sample problem, a specific satellite configuration that has been studied in a previous investigation using numerical integration techniques. Our results show remarkable agreement both qualitatively and quantitatively with published data obtained from the numerical integration techniques.
A Thesis in Mathematics submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy (PhD), 2005