Formulation of governing equations for an elastic cable have a long and dated history. A unified framework to detect the dynamics of such systems is detailed, justified and assessed numerically. Modal analyses are performed in the Frenet basis which parts the motion into the local frame and accounts accurately for the system's physics. In this article, a methodology to produce arbitrary reduced-order models for cable nonlinear dynamics is provided. The results obtained from the latter via direct time integration are challenged numerically via a comparison with results of nonlinear finite element method.