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.