Lie groups and Lie algebras are used to research the dynamics and computed torque law control of free flying space robot systems. First the adjoint transformations and adjoint operators of Lie groups and Lie algebras are discussed. Then the free flying base systems are transformed to fixed base systems. The inverse dynamics and forward dynamics are described with Lie groups and Lie algebras. The computed torque control law is used to simulate with the results of dynamics. The simulation results show that with the method the dynamical simulation problems of space robot can be solved quickly and efficiently. This built the foundation of real-time control based on dynamics. The computed torque control law has good performance.