Dear all,

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.
```

Regards,

Ran