Abstract: The impact dynamics of a free-floating flexible space manipulator capturing a moving satellite, and unstable space manipulator control after impact are analyzed. Firstly, the elastic deformation of flexible link is described approximately with assumed mode method, and a dynamic model of the flexible space manipulator multi-body system is derived by combining the second Lagrange equation. Based on the momentum conservation theory, the impact dynamics between the space manipulator and satellite is analyzed with momentum-impulse method. For the unstable space manipulator system after impact, a composite control of robust stabilization and adaptive vibration suppression is designed to stabilize the combined space manipulator and satellite system. Finally, the simulation results reveal the impact effect and validate the proposed control algorithm.