Control of nonlinear spacecraft attitude motion via state augmentation, Lyapunov-Floquet transformation and normal forms

This article analyzes and controls the quasi-periodic attitude motion of a gravity-gradient stabilized spacecraft in eccentric orbit by way of system states augmentation, Lyapunov-Floquet transformation and normal forms simplification. Perturbing torques in the ambient space environment can be shown to engender spacecraft attitude motion represented by nonlinear dynamics coupled in the roll-yaw axes; and, uncoupled planar dynamics in the pitch axis. The non-planar dynamics equations are homogeneous and analytically solvable. However, the pitch attitude motion is nonlinear, possesses parameter-varying coefficients and is subjected to external periodic excitations. Consequently, we transform the unwieldy attitude dynamics into relatively more amenable schemes for analysis and control law synthesis. Subsequently, we demonstrate the implementation of linear and nonlinear control laws (i.e. bifurcation and sliding mode control laws) on the relatively acquiescent transformed attitude dynamics. By employing a two-pronged approach, the quasi-periodic planar motion is independently shown to be stabilizable via the nonlinear control approaches.