I am diving in the source code of Moordyn. And when initializing the mooring line shape, Moordyn will call subroutine ‘catenary’ to use the analytical solution to calculate the initial shape.
But I am not familiar with the adopted formulas. Would anyone suggest some relevant papers which derived the analytical solution for mooring line?
Below is the description for subroutine catenary:
SUBROUTINE Catenary ( XF_In, ZF_In, L_In , EA_In, & W_In , CB_In, Tol_In, N , & s_In , X_In , Z_In , ErrStat, ErrMsg ) ! This subroutine is copied from FAST v7 with minor modifications ! This routine solves the analytical, static equilibrium equations ! for a catenary (or taut) mooring line with seabed interaction. ! Stretching of the line is accounted for, but bending stiffness ! is not. Given the mooring line properties and the fairlead ! position relative to the anchor, this routine finds the line ! configuration and tensions. Since the analytical solution ! involves two nonlinear equations (XF and ZF) in two unknowns ! (HF and VF), a Newton-Raphson iteration scheme is implemented in ! order to solve for the solution. The values of HF and VF that ! are passed into this routine are used as the initial guess in ! the iteration. The Newton-Raphson iteration is only accurate in ! double precision, so all of the input/output arguments are ! converteds to/from double precision from/to default precision.