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As space robots gain more and more importance in space operations, it was becoming imperative to understand their distinctive dynamics. The dynamics model of the space flexible robots is very complex, and the differential equation derived from dynamics was solved difficultly and slowly. In this paper the dynamics of space flexible robots was discussed, and the fast efficient integration method was used to solve this complex differential equation. Simulations results show that the dynamic modeling and fast efficient numerical integration techniques of flexible space robot proposed in this paper are very useful.