This dissertation is devoted to the problem of attitude control of a rigid body and its applications, a problem that arises such as spacecraft,robotics,vehicles,and weapon systems.The main results and contributions are as follows:1.The quaternion is used to globally or almost globally represent the attitude of a rigid body. The problem of attitude stabilization is formulated to form a framework for controller development.2.The problem of attitude stabilization is studied for large angle maneuvers. Two designs are presented. First , a geometric approach based on stable zero dynamics is proposed, which leads to family of system parameter dependent controllers that ensure the stability of the resulting closed loop system. Second, control laws derived from the Lyapunov technique are presented which ,again, guarantee the closed loop stability, but without canceling nonlinearities ,and are hence independent or system parameters.3.Apllys above method in three-axis turn-able platform of the fixed air balloon, then the mechanism model and attitude control of it are examined. The simulation on the three-axis turn-able platform uses classic Runge桲utta algorithm by C language.4.The feedback linearization of lvlIMO nonlinear control system is simply researched. The discoupled method is used in controlling the three-axis turnable platform and has a fine result.