Stability Solution to Linearized Equations of Motion for a Symmetric Spinning Satellite in an Elliptical Orbit Applied to the Non-Linear Equations

摘要

The attitude of a spinning symmetrical satellite in an elliptical orbit is analyzed. The perturbed motion of the satellite is described by linear equations with periodic coefficients. Stability is determined by Floquet theory. Active control is added to the system and results lead to a linear periodic control law. Scalar control from the linearized system is implemented to evaluate the performance of the control law on the non-linear equations of motion. For small disturbances, it is illustrated the controlled non-linear response duplicates the linear case. For larger disturbances, phase portraits show the resulting behavior of the coupled modes. As the perturbed motion increases in magnitude stability regions appear. Initial motion results either a return to the initial equilibrium, an oscillation around the equilibrium point or divergence from the initial equilibrium. Keywords: Satellite attitude, Equations of motion, Floquet theory, Modal control theory, Elliptical orbit trajectories, Spin stabilization, Theses. (JHD)