## 1 Introduction  
The behaviour of ships sailing in waves is of utmost importance for safety from an intact stability point of view [1]. For this reason, the International Maritime Organization (IMO) developed the Second Generation Intact Stability Criteria (SGISC) to cover five failure modes that may occur in all vessels [2, 3]. However, even on ships that meet existing stability criteria, accidents still occur [4]. However, in most cases, the seakeeping operability criteria related to roll motion and lateral acceleration can help in preventing the ship from experiencing dangerous situations due to roll synchronism, since they set limits low enough to allow people on board to work. Of the six degrees of freedom, the rolling motion is the most important from the point of view of periodicity, amplitude of angles and accelerations [5]. In fact, one of the five failure modes in SGISC is the excessive acceleration criterion, which deals with the lateral acceleration experienced on board. This criterion was introduced in the SGISC framework later than the other four failure modes and as a consequence of a submission from Germany, which noted that lateral acceleration due to synchronous rolling was not addressed by the other four SGISC [6]. This rolling motion is directly related to the above-mentioned intact ship stability because the ship's natural rolling period (Td) is inversely proportional to the square root of the metacentric height (GM), i.e., the ship's loading condition, and directly proportional to the beam of the ship. [PERSON] et al. [7] proposed an interesting system to monitor lateral acceleration and estimate the extreme values that could occur, especially sailing in beam waves and at low speed. To test the system, a mid-sized stern trawler was selected, showing that the operability criterion for lateral acceleration is exceeded in many sea-state conditions. If the ship encounters a series of waves where its natural rolling period matches the wave period, synchronous rolling can occur, and the vessel will not have time to right itself before the next wave strikes [8]. If this situation is not previously detected by ship operators, it can result in the ship's capsizing, with disastrous consequences for the safety of the ship, its crewmembers, its cargo and the environment [9; 10]. Therefore, when ships are close to reaching the transversal synchronism phenomenon, they are in serious danger because they may roll over beyond a point from which they cannot return to the upright position, resulting in capsizing [11]. Other dangers associated with this problem are water washing over the deck, which is especially dangerous for small fishing vessels with low weather decks [3], or cargo shifting on merchant ships, which can result in loss of stability and, finally, capsizing. Furthermore, excessive rolling can cause cargo lashings to give way, resulting in cargo damage and, in some cases, structural damage to the ship [12]. Therefore, in spite of not being studied as much as other phenomena such as parametric resonance, synchronous rolling is a typical experience for almost all sailors. For this reason, researchers such as [PERSON] et al. [13] studied the procedure for the measurement of the ship's natural rolling period (Td) during navigation. Furthermore, in order to connect the relationship of Td with the sea state, other scholars such as [PERSON] et al. [14] addressed the estimation of sea state during the sea route in order to predict wave-induced ship motions. In view of the development of autonomous merchant ships, [PERSON] et al. [15] proposed a new method for detecting and avoiding dangerous phenomena on board these vessels due to excessive motion as a consequence of the synchronous roll produced in rough seas. With this approach, remote operators have sufficient time to react to avoid large rolling angles and capsizing. However, although it is very interesting research, it is important to notice that, at present, the consequences of synchronism still occur in non-autonomous ships.