Dynamics of a deep-sea cable system

We consider the problem of the dynamics of a deep-sea cable system consisting of branches of constant and variable length, interacting with an undercurrent which is variable in depth and direction. We construct a mathematical model for the motion of the element of the cable system. The cables are modeled as inextensible, flexible filaments of variable length. For numerical realization of the problem, we suggest special regularizing transformations of the variables, making it possible (without additional simplifications) to take into account all the characteristic features of the motion of the filaments and to avoid difficulties in the integration of the equations of motion connected with the variability of the length of the branches of the cable system. The proposed mathematical model and the technique for its numerical analysis is applicable for the investigation of the dynamics of a complex for mining minerals from the ocean floor