Marine cables under low tension and torsion on the sea floor can undergo a dynamic buckling process during which torsional strain energy is converted to bending strain energy. The resulting threedimensional cable geometries can be highly contorted and include loops and tangles. Similar geometries are known to exist for supercoiled DNA (deoxyribonucleic acid) and these also arise from the conversion of torsional strain energy to bending strain energy or, kinematically, a conversion of twist to writhe. A dynamic form of Kirchhoff rod theory is presented herein that captures these nonlinear dynamic processes. The resulting theory is discretized using the generalized-α method for finite differencing in both space and time. The important kinematics of cross-section rotation are described using an incremental rotation “vector” as opposed to traditional Euler angles or Euler parameters. Numerical solutions are presented for an example system of a cable subjected to increasing twist at one end. The solutions show the dynamic evolution of the cable from an initially straight element, through a buckled element in the approximate form of a helix, and through the dynamic collapse of this helix through a looped form.

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