Based on the original quadrotor UAV (unmanned aerial vehicle) elastic hanging model, this paper introduces the concept of the direction vector of the hanging load according to the attitude of the UAV hanging load, and redefines the elastic hanging model of the quadrotor UAV. Then, according to the obtained new model, a brand new control law using the energy analysis method is corroborated by research through Lyapunov’s theory. The astringency of the designed quadrotor model and control method is analyzed by the Lassalle invariance principle, and the whole system designed in this paper is summarized and analyzed, and the correctness of the derivation theory is proved. To prove feasibility and astringency of the designed elastic rigging system and controller, the whole system is simulated to verify the feasibility of the experimental theory. Finally, all the above work is summarized, the shortcomings of the designed system model are analyzed, and the future research focus and direction are determined.