A hybrid turbine engine, comprising: a first thrust-generating device that includes a turbine, wherein the turbine includes a turbine rotary shaft; a clutch including a clutch input, which is operatively coupled to the turbine rotary shaft, and a clutch output, wherein the clutch defines: (i) an engaged state in which the clutch input is rotationally coupled to the clutch output; and (ii) a disengaged state in which the clutch input is rotationally decoupled from the clutch output; a rotary electric machine including a machine rotary shaft, which is operatively coupled to the clutch output; a second thrust-generating device that is operatively coupled to the machine rotary shaft; and an electric power system; wherein the rotary electric machine is configured to: (i) selectively receive an electric power input from the electric power system and generate an output torque to rotate the second thrust-generating device, via the machine rotary shaft, responsive to receipt of the electric power input; and (ii) selectively receive an input torque from the machine rotary shaft, to generate an electric power output responsive to receipt of the input torque, and to provide the electric power output to the electric power system, wherein the clutch includes a synchronization structure configured to synchronize the clutch input and the clutch output prior to permitting the clutch to transition from the disengaged state to the engaged state, the synchronization structure including a speed controller configured to control a rotational frequency of the rotary electric machine to synchronize the clutch output to the clutch input. a first thrust-generating device that includes a turbine, wherein the turbine includes a turbine rotary shaft; a clutch including a clutch input, which is operatively coupled to the turbine rotary shaft, and a clutch output, wherein the clutch defines: (i) an engaged state in which the clutch input is rotationally coupled to the clutch output; and (ii) a disengaged state in which the clutch input is rotationally decoupled from the clutch output; (i) an engaged state in which the clutch input is rotationally coupled to the clutch output; and (ii) a disengaged state in which the clutch input is rotationally decoupled from the clutch output; a rotary electric machine including a machine rotary shaft, which is operatively coupled to the clutch output; a second thrust-generating device that is operatively coupled to the machine rotary shaft; and an electric power system; wherein the rotary electric machine is configured to: (i) selectively receive an electric power input from the electric power system and generate an output torque to rotate the second thrust-generating device, via the machine rotary shaft, responsive to receipt of the electric power input; and (ii) selectively receive an input torque from the machine rotary shaft, to generate an electric power output responsive to receipt of the input torque, and to provide the electric power output to the electric power system, (i) selectively receive an electric power input from the electric power system and generate an output torque to rotate the second thrust-generating device, via the machine rotary shaft, responsive to receipt of the electric power input; and (ii) selectively receive an input torque from the machine rotary shaft, to generate an electric power output responsive to receipt of the input torque, and to provide the electric power output to the electric power system, wherein the clutch includes a synchronization structure configured to synchronize the clutch input and the clutch output prior to permitting the clutch to transition from the disengaged state to the engaged state, the synchronization structure including a speed controller configured to control a rotational frequency of the rotary electric machine to synchronize the clutch output to the clutch input.