In air–water interface towing systems (AWITS), the cable simultaneously spans air and water and is subjected to discontinuous loads at the free surface. When cable deployment and retrieval are involved, the system exhibits pronounced unsteady coupled responses, posing significant challenges to motion prediction and control design. To address this problem, this paper establishes a flexible multibody dynamic framework for AWITS with time-varying cable length. Based on the arbitrary Lagrangian–Eulerian Absolute Nodal Coordinate Formulation, a variable-length trans-free-surface cable element is developed, enabling a unified treatment of discontinuous loads near the air–water interface during reeling operations. A complete coupled dynamic model of the towed vehicle, array cable, and drogue is further constructed and validated through a wave–current loading case, a variable-length pendulum case, cross-medium towing experiments, and comparisons with existing numerical results. The results show that the initial underwater-to-aerial cable-length ratio, Sw, as a descriptor of time-varying hydrodynamic effects, is a key parameter governing the unsteady configuration evolution of the system. Under large-amplitude reeling conditions, cable tension and towed vehicle attitude are strongly coupled, and a larger Sw increases the sensitivity of the system configuration to towing speed and reeling speed. Under small-amplitude periodic reeling conditions, reducing the reeling period significantly intensifies harmonic disturbances near the free surface and induces stronger pitch responses at smaller Sw. This work provides a theoretical basis for dynamic analysis, motion prediction, and control design of AWITS.
Liu et al. (Fri,) studied this question.