The　impact　dynamics　and　post-impact　control　for　stabilizing　of　a　free-floating　space　manipulator　capturing　an　unknown　motion　satellite　are　studied.　The　dynamical　models　of　the　space　manipulator　and　satellite　are　separately　derived　from　second　Lagrange　equation　and　Newton-Euler　equation;　the　impact　effect　is　calculated　base　on　kinematics　and　impact　force　transmission　relationship;　after　the　satellite　capturing,　by　combining　the　above　dynamics　models　of　space　manipulator　and　satellite,　the　post-impact　dynamics　model　of　the　combinational　system　is　presented;　and　then　an　augmented　robust　control　algorithm　is　designed　for　stabilizing　the　motion　of　the　post-impact　combinational　system.　This　control　can　be　employed　under　the　space　manipulator　base＇s　position　uncontrolled,　and　the　control　equation　still　keep　linear　for　the　uncertain　satellite　parameters.　Finally,　the　simulation　results　show　the　system　motion　state　of　the　capture　process,　and　verify　the　validity　of　the　above　robust　control　for　stabilizing.