A new dynamic model of towing cables - da Silva Gomes, Samuel; Pinheiro Gomes, Sebastião Cícero (Ocean engineering, 2021)
This article proposes a new formalism for the dynamic modeling of a cable towing system, in which both the tugboat and the towed vessel are subject to forces from waves on the sea surface. The continuous flexibility of the cable is approximated by a discrete equivalent, formed by rigid links connected by fictitious elastic joints that allow elevation movements, since the dynamics are restricted to the vertical plane. The Euler-Lagrange formalism was used to determine the dynamic models considering two, three and four links. The growth patterns of the differential equations of the models were found, thus allowing the development of generic algorithms, capable of generating dynamic models considering any number of links. Vertical forces obtained from proportional and derivative control were applied to the tugboat and the towed vessel, thus simulating the wave motion of the sea surface. Simultaneously, a motor thrust is applied to the tugboat. An algorithmic procedure is also proposed to determine the dynamic tension in the cable. Simulation results showed dynamic responses as physically expected. Computer animations made from simulation data show a great sense of physical reality. •Dynamic cable modeling.•Proposition of a new discreet dynamic modeling formalism.•Application to problems related to towing vessels.•Proposition of a method to calculate the dynamic tension in the cable.