  We used binary octahedrons to investigate the dynamical behaviors of binary
asteroid systems. The mutual potential of the binary polyhedron method is
derived from the fourth order to the sixth order. The irregular shapes,
relative orbits, attitude angles, as well as the angular velocities of the
binary asteroid system are included in the model. We investigated the relative
trajectory of the secondary relative to the primary, the total angular momentum
and total energy of the system, the three-axis attitude angular velocity of the
binary system, as well as the angular momentum of the two components. The
relative errors of total angular momentum and total energy indicate the
calculation has a high precision. It is found that the influence of the orbital
and attitude motion of the primary from the gravitational force of the
secondary is obvious. This study is useful for understanding the complicated
dynamical behaviors of the binary asteroid systems discovered in our Solar
system.
