Possible simplified mathematical models for roll motion in the development of performance-based intact stability criteria \u2013 Extended and revised version

In this paper a mainly analytically based approach is presented to deal with the problem of intact ship stability in regular and irregular waves for two conditions: beam and longitudinal sea. The paper is oriented at providing simplified physically sound 1-DOF analytical models to be incorporated in a regulatory framework and for this reason a balance is sought between simplicity and accuracy. When possible, approximate analytical methods are proposed in order to try avoiding, as much as possible, direct numerical simulations. In the case of non-deterministic models, both the short-term and the log-term aspects of the problem are analysed. When analytical estimations of the capsize probability are not available, semi-empirical approaches are proposed. The paper is to be intended as a series of proposals needing additional check and validation as a further development