Aiming at the asteroid 1996 HW1, this paper is devoted to stabilizing the relative motions by Hamiltonian structure-preserving control. Firstly, the asteroid 1996 HW1 is modeled as a contact binary asteroid, consisting of a sphere in physical contact with an ellipsoid, which captures the main characteristics. By linearization of equations of motion near the equilibrium points (abbr. EPs), analytical results show that in planar cases, two collinear EPs are saddles with one-dimensional stable/unstable manifolds and two dimensional center manifolds, referred to as 1+1+2 type while two non-collinear EPs are unstable with two-dimensional stable manifolds, two-dimensional unstable manifolds and zero-dimensional center manifolds, referred to as 2+2+0 type. Subsequently, by implementing complex diagonal matrix decomposition upon the corresponding symplectic matrix the stable/unstable manifolds of non-collinear EPs are refined to stabilize the system with different gains. As for collinear EPs, the stable/unstable manifolds as well as center manifolds are utilized. Furthermore, it is analytically proven that the poles of the system can be arbitrarily assigned on the imaginary axis by this controller. The stable Lissajous orbits and samples of periodic orbits are yielded numerically.
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