Relative equilibria and bifurcation of a dumbbell spacecraft about an asteroid with gravitational orbit-attitude coupling

Space missions to asteroids have played an important role in the scientific exploration of the solar system. The spacecraft dynamics about asteroids is fundamental for the mission design. In the present paper, relative equilibria and their bifurcation in the gravitationally coupled orbit-attitude dynamics (full dynamics) of a dumbbell spacecraft about an asteroid is studied. By using geometric mechanics, the full dynamics of the dumbbell spacecraft in the gravity field of the asteroid is derived. Then, the orbit-attitude relative equilib-ria about asteroids 4769 Castalia, 433 Eros, and 6489 Golevka are obtained by solving the condition of stationary points of the Lagrangian. The orbit-attitude equilibria of the dumbbell spacecraft provide natural positions for large tethered satellite hovering over the asteroid surface. Compared with the classical equilibrium points of the orbital motion of a point mass, it has been found that a classical point-mass equilibrium point can generate three orbit-attitude equilibria located nearby. Finally, the bifurcation of the orbit-attitude equilibria with respect to the dumbbell spacecraft's dimension is also presented.