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In this paper, a Nonsingular Terminal Sliding Mode Control (NTSMC) strategy is investigated to address the finite-time attitude tracking problem of a rigid spacecraft. Hybrid thruster and flywheel actuator system is used for rapid reorientation under external disturbance. The reference torque is obtained from time-optimal attitude trajectory, and it is exerted on the satellite by thrusters in the form of feedforward compensation. Owing to thruster output torque deviation, initial measurement error and external disturbances, the practical trajectory of a satellite would deviate from reference trajectory. In order for the satellite to track the reference trajectory in finite time, the correction torque is deduced based on the error between reference trajectory and real-time measurements, and then applied through flywheels in the form of feedback compensation. The NTSMC method is used to solve nonsingular problem and to improve the control precision of the satellite attitude tracking issue. The numerical simulation results show that this control strategy is effective and it has great robustness. [ABSTRACT FROM AUTHOR]