The　impact　dynamics　model　of　space　manipulator　capturing　a　satellite　on　orbit　is　derived,　during　the　post-impact　process,　a　calming　motion　control　with　RBF　neural　network　and　an　active　suppression　for　flexible　vibration　are　discussed.　In　pre-impact　process,　according　to　the　assumptive　model　method　and　Lagrangian　equation,　the　dynamics　model　of　space　manipulator　system　is　derived.　In　impact　process,　considering　the　kinematic　and　force　transfer　relationship　between　the　space　manipulator　and　satellite,　and　base　on　the　momentum　conservation,　the　impact　effect　for　the　rigid　motion　and　flexible　vibration　of　the　space　manipulator　system　is　analysed.　In　post-impact　process,　considering　the　interaction　of　space　manipulator　and　target　satellite,　the　synthesized　dynamics　model　of　both　is　derived,　for　the　impact　effect,　base　on　the　singular　perturbation　theory,　the　synthesized　dynamics　model　is　decomposed　into　a　fast　subsystem　which　represents　the　assembly　system＇s　flexible　vibration,　and　a　slow　subsystem　which　represents　the　assembly　system＇s　rigid　motion.　A　RBF　neural　network　control　is　designed　for　calming　rigid　motion;　a　linear　quadratic　optimal　control　is　designed　for　suppressing　flexible　vibration.　The　simulation　results　show　the　efficiency　of　the　controls.　©　2014　Journal　of　Mechanical　Engineering.