Numéro : 2049 - Year : 1987
Dynamical study of submarine bodies towed by cables of variable length
D. MARICHAL, Professeur
B. DASSONVILLE, Ingénieur, au Laboratoire d'Hydrodynamique Navale, Ecole Nationale Supérieure de Mécanique de Nantes
O. LEFORT, Ingénieur, au Laboratoire d'Hydrodynamique Navale, Ecole Nationale Supérieure de Mécanique de Nantes
Carrying on our studies on towed submarine systems. we generalized our computation methods 10 the case where the cable length 15 not a constant (winch driving) .It is now possible to study the way the submarine body 15 put Into and taken out of the water. It is also expected to use this method to define laws governing the cable winding which would reduce platform movements of a tower.
This study concerns systems whose elements and movements are always In a vertical plane ( twodimensionnal problem) .
The differential equations. describing the cable dynamics. are obtained on the one hand from Lagrange equations with multipliers for the submerged part of the cable and on the other hand from .momentum. equations for the part which passes through the pulley. These equations are made complete by conditions on the cable length conservations. A finite difference scheme gloves the velocities and accelerations at time the In any points of the cable as functions of their coordinates at time t-2h. t-h and t. Assuming that these coordinates are known at time t-2h. t-h and t. one can obtain a system of equations predicting their values at time t+h. A special organisation of this system of equations allows for a very fast solution at each time step using an Iterative method which prevents from using liberalisation techniques on the length conditions .