Tethered structures have widely appeared in mechanical components due to their flexibility and lightweight characteristics. In aerospace engineering, aerial vehicles employ tethers as crucial components for towing, refueling, and exploration missions. Tethered structures form flexible multibody systems, and their dynamic motion can significantly influence the overall system behavior [1,2]. This study focuses on the transient dynamics of a tether attached to an aerial vehicle during deployment and retrieval processes. A numerical dynamic model is established by combining a variable-length flexible cable model based on an arbitrary Lagrangian-Eulerian absolute nodal coordinate formulation (ALE-ANCF) with a rigid-body attitude model described using Euler parameters. Torsional effects in the cable are newly incorporated, and their dynamic influence on both the cable motion and the attitude of the rigid body is investigated. In conventional ALE-ANCF approaches, elements are inserted or removed when their lengths exceed prescribed thresholds, which can lead to numerical disturbances. To enhance numerical stability, a co-moving node strategy is proposed, in which adjacent nodes are advanced in tandem with node deletion. Numerical results demonstrate that the proposed method effectively captures the dynamic behavior of the tether and the aerial vehicle.