Computational phase portrait analysis of two nonlinear small satellite models

Two small satellite models are selected that are subject to gravity gradient in circular, low-altitude orbits. The second one is passively controlled by a pitch momentum wheel. The aim of this work is to represent how the passive pitch bias momentum method affects the nonlinear attitude dynamics. The analysis is based on phase portraits, Poincaré sections, and time responses. The phase portraits show that there are multiple equilibrium points lying on the Euler angle axes. Global behaviors remind motion about a saddle point located at the origin. The dynamics of the second model seems to have reduced nonlinear characteristics according to corresponding, less attracted motion pattern compared to the pattern for the first model observed in phase portraits and according to scattered points that do not build island-like structures, which is the case for the first model, in Poincaré sections. The time responses obtained using low initial attitude angles indicate that the nonlinear responses of the second model bring stable nonlinear motion to mind whereas the responses of the first model are divergent, so unstable. The pitch momentum wheel induces nutation that leads to high-frequency oscillation besides the low-frequency oscillation.