Analysis of the attitude dynamics of a spacecraft on a stationary orbit around an asteroid via Poincaré section

Attitude dynamics of spacecraft subjected to the gravity gradient torque is a fundamental problem in the astrodynamics and 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 of a rigid spacecraft 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 a kind of generalized Poincaré section is then utilized to investigate the dynamical behavior of the nonlinear equations of attitude motion. The generalized Poincaré section technique is used to trace differences between the torque-free attitude motion and the gravity-gradient-perturbed motion. The effects of the coefficients C20 and C22 of the non-central gravity field of the asteroid are especially concerned. We find that under the perturbation of the gravity gradient torque, the attitude motion is significantly chaotic. We also find that due to the non-central gravity field of the asteroid, the attitude dynamics of the spacecraft is modified significantly in comparison with the classical attitude dynamics on a circular orbit in a central gravity field.