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This paper studies unmanned aerial vehicle (UAV)-enabled wireless communication, where a rotary-wing UAV is dispatched to communicate with multiple ground nodes (GNs). We aim to minimize the total UAV energy consumption, including both propulsion energy and communication related energy, while satisfying the communication throughput requirement of each GN. To this end, we first derive a closed-form propulsion power consumption model for rotary-wing UAVs, and then formulate the energy minimization problem by jointly optimizing the UAV trajectory and communication time allocation among GNs, as well as the total mission completion time. The problem is difficult to be optimally solved, as it is non-convex and involves infinitely many variables over time. To tackle this problem, we first consider the simple fly-hover-communicate design, where the UAV successively visits a set of hovering locations and …