## 1. Hydrodynamic interaction between bodies

This option enables the user to include hydrodynamic interaction effects between an arbitrary number of bodies. These effects may be significant in case the distance between the floating bodies is small.

The hydrodynamic interaction effects affect the first and second order wave excitation forces and the added mass- and damping-forces. The effects on the wave excitation forces are included as part of the body forces, see Body forces, while the effects on frequency-dependent added mass- and damping-forces are included in coupled retardation functions and coupled added mass at infinite frequency.

By introducing the coupled added mass at infinite frequency into the equation of motion, the inertia term is written

where the indices \(\mathrm {i}\) and \(\mathrm {j}\) refer to body \(\mathrm {i}\) and body \(\mathrm {j}\). \(\mathrm {\boldsymbol{\ddot {x}}_i}\) and \(\mathrm {\boldsymbol{\ddot {x}}_j}\) are accelerations in 6 DOF referring to the respective body-fixed coordinate systems.

Symmetric mass properties are assumed, that is

The term associated with the retardation functions is written

The implemented formulation makes use of symmetric properties