Abstract: Among various attitude representations of rigid body,the Euler angles, Cardan angles and Euler parameters are applied frequentlyin engineering. Recently the application of Rodrigues parameters in theattitude control of spacecraft attracts some attention. The Rodriguesparameters have some distinctive advantages of simplicity inrepresentation and their algebraic calculation. In the space flightpractice, it isdifficult to determine the accurate value of dynamical parameters of aspacecraft in orbit, then the adaptive behavior of attitude control isrequired to adapt the variation of parameters. In the present paper thedynamical equations of controlled attitude motion of a torque-free gyrostatexpressed by Rodrigues parameters are derived, and an adaptiveapproach based on Rodrigues parameters is proposed to keep a predeterminedattitude under the internal disturbance. The Lyapunov theorem is used toprove the asymptotic stability of the controlled motion.