The　on-orbit　satellite　maintenance,　refuelling　or　retrieve　are　the　main　servicing　assignments　of　space　manipulator,　the　rendezvous　and　docking　between　space　manipulator　and　satellite　is　inevitable　when　on-orbit　servicing.　In　this　paper,　the　impact　dynamics　in　rendezvous　and　docking　of　free-floating　space　manipulator　capturing　a　target　satellite　is　discussed,　and　the　post-impact　dynamic　control　of　the　space　manipulator　and　target　satellite　mix-bodies　system　is　presented.　Firstly,　base　on　the　assume　modes　method,　the　flexible　link　elastic　deformation　is　described,　and　combining　the　Lagrange　formulation,　the　dynamic　formulation　of　free-floating　flexible　space　manipulator　system　is　derived;　and　the　target　satellite　is　assumed　as　a　single　rigid　body,　the　dynamic　formulation　of　the　target　satellite　is　derived　by　Newton-Euler　formulation.　Secondly,　base　on　the　above　dynamic　formulations,　and　focus　on　the　impact　during　the　rendezvous　and　docking　of　free-floating　flexible　space　manipulator　capturing　a　target　satellite,　the　impact　effect　is　calculated　by　the　momentum　impulse　method,　this　is　the　impact　dynamics.　Finally,　focus　on　the　unstable　post-impact　state　of　space　manipulator　and　target　satellite　mix-bodies,　the　feedback　control　is　applied　for　calming　the　rigid　motion,　and　linear　quadratic　optimal　control　is　applied　meanwhile　for　suppressing　the　flexible　vibration　of　flexible　link.　The　simulation　result　reveals　the　impact　effect,　and　verifies　the　effectiveness　of　the　above　control.　Copyright　©　2013　by　the　International　Astronautical　Federation.　©2013　by　the　International　Astronautical　Federation.　All　rights　reserved.