A major limitation of existing battery-powered quadrotor UAVs is their reduced flight endurance. To address this issue, by leveraging the electrical model of a brushless DC motor, we explicitly determine minimum-energy paths between a predefined initial and final configuration of a quadrotor by solving an optimal control problem with respect to the angular accelerations of the four propellers. As a variation on this problem, if the total energy consumption between two boundary states is fixed, minimum-time and/or minimum-control-effort trajectories are computed for the aerial vehicle. The theory is illustrated for the DJI Phantom 2 quadrotor in three realistic scenarios.