Analysis of gravity-gradient-perturbed attitude dynamics on a stationary orbit around an asteroid via dynamical systems theory

Attitude dynamics of spacecraft subjected to the gravity gradient torque is a fundamental problem in the space engineering. The interest in asteroid missions for the scientific exploration and near-Earth object (NEO) hazard mitigation has been increasing ever since the last two decades. The studies on attitude dynamics of spacecraft around asteroids are necessary for the design of the attitude control system. In this paper, the full nonlinear attitude dynamics on a stationary orbit around a uniformly-rotating asteroid is analyzed via the canonical Hamiltonian formalism and the dynamical systems theory. The nonlinear equations of attitude motion are obtained by Hamilton's canonical equations, in which the perturbations due to the gravity gradient torque and the precession of the orbital frame are both considered. A numerical method using the Poincaré section is then utilized to investigate the nonlinear equations of attitude motion. The Poincaré section technique is used to trace differences between the torque-free motion and the gravity-gradient-perturbed motion. The effects of the coefficients C20 and C22 are especially concerned. We find that under the perturbation of the gravity gradient torque, the motion is significantly chaotic. We also find that due to the non-spherical shape of the asteroid, the attitude dynamics is modified significantly in comparison with the classical attitude dynamics on a circular orbit in a central gravity field.