Mathematical models in description of capsizing scenarios

Nowadays, although the knowledge of the causes of capsizing is more and more vast, still the large quantities of ships sink as a result of capsizing accidents. Therefore, this particular subject is widely discussed in the paper as a major issue among many prominent research centres. Presently, the results of the numerical simulations represent the most important part in these debates. This paper is my first attempt to demonstrate some of the main mathematical models used in hydrodynamics to describe different scenarios of capsizing. Generally, the article concentrates on non-linear models due to the fact that they are widely employed to practical calculations. These models are used both for capsizing tests and, very often, for judging design parameters, such as slamming, green-water-on-deck, etc. The choice of mentioned scenarios was made according to their frequency in real circumstances.