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In order to deal with the complicated problem of orbit and attitude control of a flexible spacecraft，a study of dynamic modeling and control of flexible spacecraft is conducted. A new dynamic model which can describe the orbit and attitude dynamics of flexible spacecraft at the same time is proposed, using the method of dual quaternions. The new dynamic model is able to describe the orbit and attitude of the spacecraft integrally, and to consider the coupling effect between the vibration of the flexible parts of the spacecraft and its translation and rotation automatically. An adaptive position and attitude-tracking controller which requires no information of the spacecraft's inertial parameters is designed based on the model. The coupling effect of the flexible parts can be estimated using the adaptive controller, and thus the stability of the whole system during orbit and attitude maneuver process is improved. The simulation result demonstrates that the adaptive controller fits the problem of orbit and attitude control for flexible spacecraft well and thus is applicable. [ABSTRACT FROM AUTHOR]