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The next-generation space missions, such as the space moving target tracking mission and the agile attitude maneuvering mission and so on, propose a high requirement on spacecraft attitude control system. For such missions, hybrid attitude control actuators consisting of control moment gyro and reaction wheel, which can not only offer large control torque but also achieve high control precision, is the best alternative choice. For this hybrid actuator system, the angular momentum management is vital. To handle the momentum management problem, an optimal angular momentum strategy based on cooperative game theory is proposed. The cooperative game model is constructed according to the quadratic programming problem to achieve the minimization of control moment gyro gimbal angular speed and reaction wheel angular acceleration. The proposed cooperative game theory steering logic has overcome the control moment gyro singular problem and reaction wheel saturation problem of the hybrid system. In addition, the energy cost of the hybrid actuator system is reduced. Five groups of simulation scenarios are carried out to demonstrate the effectiveness of the proposed steering logic.