  In high-speed maritime operations, the broaching phenomenon can pose a
significant risk when navigating in following/quartering seas. The occurrence
of this phenomenon can result in a violent yaw motion, regardless of the
steering effort, which, in turn, cause the resulting centrifugal force to
capsize a vessel. A necessary condition for the occurrence of broaching is the
surf-riding phenomenon. Therefore, the International Maritime Organization
(IMO) has set up criteria to include theoretical formulas for estimating the
occurrence of surf-riding phenomena. The theoretical equation used in the IMO's
second-generation intact stability criteria (SGISC) to estimate the surf-riding
threshold is based on Melnikov's method. This paper presents nonlinear
equations describing the forward and backward motions of a ship. However, such
equations cannot be directly solved; therefore, we proposed the use of and
explain various approximate solution methods, including Meknikov's method.
Subsequently, the relationship between the theoretical prediction method of the
surf-riding threshold rooted in Melnikov's method and the IMO's SGISC is
determined.
