Abstract
Discrete models for the determination of cable shapes and tensions require the solution of large systems of nonlinear algebraic equations. In these the unknowns are the orientations and coordinates of the segments as well as their tensions. Smaller systems of algebraic equations are obtained by the pre-elimination of the tensions and the coordinates for the lumped mass and rod models which leave the orientation variables as the only unknowns. Furthermore, this pre-elimination analysis yields conditions for the equivalence of the lumped mass and the rod models. This method is applied to the determination of the position of a towed underwater sensor used for seabed mapping or for oceanographic recordings.
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