Summary: ON DYNAMICAL SYSTEM THEORY APPLICATION TO EARTH-SATELLITE PITCH
AUTHOR: Emmanuel Osei-Frimpong - KNUST
ABSTRACT: In this paper, an analytic method for solving a differential equation which represents
the dynamics of Pitch Attitude librations of an orbiting earth-satellite is discussed. This highly non linear
equation of motion of the Pitch Attitude librations is transformed into a system of equations in terms of the
The scheme applies Dynamical Systems Theory by determining its equilibrium configuration or fixed
points and linearizing the governing equations about these fixed points. In most cases, the linearized systems
of equations have constant coefficient matrices. However, our linearized system of equations has a periodic
coefficient matrix in terms of its independent variable.
Based on the periodic nature of the coefficient matrix, the linearized system is solved using the Floquet
theory, Fourier series analysis and eigenvalue-vector method. The complete non linear solution is then
obtained by successive approximation involving the fundamental matrix. The application of our analytical
method to a sample problem yielded extremely remarkable results.