Singularities of the Frenet Frame during Dynamic Analyzing Mooring Cables Based on Lumped Mass Modeling

Lumped mass modeling of cable is widely used for dynamic analyzing mooring cables in ocean. Both motions of cables and loads acting on cables are expressed with respect to the element frames. Generally, Frenet frame, which is suitable for continuous and differentiable space curves, is widely used for the lumped mass modeling in former researches. The rotational transformation matrix is based on Euler angles of which the rotation angles are carried out by inverse kinematics. However, singularities exist in the combination of the Frenet frame and Euler angles. This paper puts forward a new element frame which is created based on vectors of element orientation and relative velocity. Comparisons with the results by the Frenet frame show this new element frame is stable and overcomes singularities well.