Relative equilibria and stability of a dumbbell spacecraft about an asteroid

Abstract

The gravitational orbit-attitude coupling becomes pronounced in spacecraft dynamics about small asteroids, due to the large ratio of the spacecraft's dimension to the orbital radius. In this study, relative equilibria and their stability of the gravitationally coupled orbit-attitude dynamics (full dynamics) of a dumbbell spacecraft about an irregular-shaped asteroid are investigated. The shape of the asteroid is represented by a homogeneous polyhedron, and its non-spherical gravity is calculated accordingly. By using geometric mechanics, the Hamiltonian structure and equations of motion of the full dynamics are derived. Then, the orbit-attitude equilibria about asteroids 4769 Castalia, 433 Eros, and 6489 Golevka are calculated numerically, respectively, and the drift of orbit-attitude equilibria with respect to the dumbbell's varying length is also discussed. By comparing with the equilibria of a point mass, it has been found that a classical point-mass equilibrium can generate three orbit-attitude equilibria located nearby. With the increase of the dumbbell's length, the effects of orbit-attitude coupling become stronger, and the orbit-attitude equilibria diverge further from the classical point-mass equilibria. The spectral stability of the orbit-attitude equilibria is determined numerically and analyzed. It has been found that the gravitational orbit-attitude coupling is likely to make the equilibria unstable in our simulations. The dumbbell is a good approximation of a spacecraft consisting of two modules that are connected by trusses, and its orbit-attitude equilibria have potential applications in asteroid proximity operations, such as body-fixed hovering.