The vertical transport system (VTS) is a key subsystem for conveying mineral slurry from the seabed to the mining vessel during deep-sea mining operations. In ultra-deepwater environments, the VTS involves coupling between rigid and flexible components, moving boundaries induced by mining-vehicle and vessel motions, and continuous variations in the effective lengths of multiple components during recovery, posing considerable challenges for dynamic modeling. This study establishes a unified rigid-flexible coupled multibody dynamic framework in which the mining vessel, rigid riser, relay station, flexible hose, umbilical cable, and mining vehicle are described within a consistent generalized-coordinate system. The component equations are assembled through geometric and material-coordinate constraints into a unified system of differential-algebraic equations. During the solution process, the material-coordinate constraints, prescribed boundary motions, and intercomponent connection constraints are updated to capture the coupled dynamic response of the system under moving boundaries, varying component lengths, and transitions between recovery phases, without reconstructing the component models. The ALE-ANCF formulation is employed to model the variable-length flexible components, allowing continuous retrieval without remeshing or node insertion while maintaining a consistent element topology. The proposed dynamic framework is validated against the analytical solution for a variable-length equal-period pendulum, OrcaFlex results, and the static and dynamic VTS responses reported in published studies. The validated model is subsequently applied to a 5 000 m VTS to analyze its dynamic responses under in-situ operation and relocation with component recovery. The results show that mining-vessel heave increases the dynamic tension of the rigid riser, whereas the hose response is modulated by the dynamic response of the relay station. During recovery, lifting the mining vehicle off the seabed markedly increases system tension fluctuations, whereas the rigid-riser retrieval velocity has a comparatively modest influence on the overall tension level. Increasing the umbilical-cable retrieval velocity helps reduce hose tension.
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