[11-17] have proposed thirteen index-three differential-algebraic equations (DAE) in the rotary crane state variables and control variables [11-17].
Kinjo, "Vibration control of load for rotary crane system using neural network with GA-based training," Artificial Life and Robotics, vol.
Hashimoto, "Optimal control of a rotary crane," Journal of Optimization Theory and Applications, vol.
 have described rotary crane dynamics in terms of redundant coordinates with an introduction of differential-algebraic equations (DAEs).
Blajer and Kolodziejczyk  have developed improved DAE equations for more precise rotary crane dynamics simulation.
Glossiotis and Antoniadis  have derived a four-degrees-of-freedom (4DOF) model for the rotary crane system, incorporating both hoisting and slewing payload motions and thus is able to handle cases where hoisting can be simultaneously applied to the rotary motion.
 developed a three-dimensional open-loop control strategy for sway-free, point-to-point maneuvers of a rotary crane. They showed that the proposed control method is effective in eliminating residual oscillations and centrifugal force influence.
Yano, "Modeling and optimal control of a rotary crane using the straight transfer transformation method," Control Engineering Practice, vol.
Their work was later extended by developing an input-shaping notch filter to reduce payload oscillation of rotary cranes excited by operator commands.