*Article* **A New Theoretical Dynamic Analysis of Ship Rolling Motion Considering Navigational Parameters, Loading Conditions and Sea State Conditions**

**José M. Pérez-Canosa, José A. Orosa \*, María Isabel Lamas Galdo and Juan José Cartelle Barros**

Department of Navigation Science and Marine Engineering, University of A Coruña, Paseo de Ronda, 51, 15011 A Coruña, Spain

**\*** Correspondence: jose.antonio.orosa@udc.es; Tel.: +34-981-167-000 (ext. 4320)

**Abstract:** Despite the IMO's efforts and the large quantity of research carried out over the years concerning the sudden loss of stability in fishing vessels, and even the damage done to merchant fleets due to cargo shifting, accidents with very relevant consequences continue to occur. This paper can be considered as a continuation of the recent research of authors which was carried out with ships in static conditions, with pure beam seas and without resistance. The aim of the present research is to provide a reference for ships' operators to improve the ship's behavior and seakeeping, to alter the ship's loading conditions or the navigational parameters (heading and speed), and even be aware of the time available to carry out these modifications before reaching dangerous situations. For this, all sea state conditions were mathematically modelled for, including the ship's rolling motion both in static and in realistic and dynamic conditions, with the waves influencing the vessel by coming from any direction. Relevant results of easy comprehension for ships' operators are shown in each of the models, which were validated with a representative real case study.

**Keywords:** rolling motion; angle of roll; waves; dynamic conditions; capsizing; vessels; operability
