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This paper considers a transportation system consisting of a quadrotor with a cable-suspended payload. The main focus of this paper is to investigate the effect of polynomial trajectories on the vibration of the cable-suspended payload and to show which polynomial trajectory results in less vibration. A mathematical analysis and a parametric study were carried out to investigate the effect of the degree of the polynomial trajectory on its kinematic behavior. A conjecture relates the degree of the polynomial trajectory and its kinematic
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