Moving cables are used for many applications in engineering structures such as cable-supported transport systems that involves mobile cables suspended between supports for moving attached vehicles. Advantages of such systems in terms of cost, footprint and energy efficiency make its urban integration as one of the solutions to meet the need for new mobilities. Because of the inherent cable's flexibility and the modification of dynamic properties during the cable movement, such systems are sensitive to the effects of perturbations and self-sustaining oscillations. The methods commonly used to describe cable dynamics are restricted to small static sag case with a predominant vertical dynamics. To accurately analyse a multi-segment mobile cable, this paper proposes an hybrid analytical-numerical strategy to deal with a general mechanical elementary model of a cable in unsteady translation formulated in curvilinear abscissa derived from the formalism of continuum mechanics. An assembly procedure permits to deal with a more complex system considering a cable loop in contact with intermediary supports and punctual loads according to different boundary conditions, considering the coupling between the vertical dynamics activated at the local scale of a span and the longitudinal dynamics activated at the scale of the whole cable loop. The translation speed and acceleration inertial effects on the system's complex modes are studied and design rules are provided to guide an optimal conception avoiding strong oscillations of the system.