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A low-altitude endoatmospheric interceptor, which is steered by aerodynamic lift and divert thruster, is investigated in this paper. The divert thrust is provided by a solid rocket engine with a single public combustion chamber and a group of nozzles around the missile. As a result, it can be used only once. To utilize the divert thruster effectively and to determine the width of the divert thruster pulse, a logic-based guidance strategy is proposed. Moreover, the decomposition of the game space is employed to analyze the appropriate initiating time of the divert thruster. Finally, the validity of the guidance strategy is tested using a realistic 2-D ballistic missile defense scenario. It is shown that, due to the sufficient utilization of the divert thruster, there is a significant improvement in the homing performance.