Equations of a Rolling Vessel Dynamic Balance

Matematika kao znanost i pomorstvo kao djelatnost prate se kroz povijest, a razvoj matematike je bitno utjecao na razvoj pomorstva. Već sama gradnja broda u osnovi ne bi bila potpuno moguća bez različitih matematičkih proračuna. Znanje matematike ima svoju primjenu i prilikom računanja kursa, stajnice i pozicije u plovidbi te u proračunima vezanim za ekonomičnost prijevoza tereta i stabilitet broda. U plovidbi brod nailazi na razne vremenske uvjete koji uzrokuju različita gibanja broda odnosno njihanja. U ovom radu objašnjena je dinamička ravnoteža njihanja matematičkim jednadžbama. Da bi razumjeli te jednadžbe potrebno je razumjeti njihanje broda kao fizikalne pojave te princip rješavanja matematičkih jednadžbi koje ih opisuju.Mathematics as a science and the shipping industry as a business have always been related to each other through the history and development of the mathematics has strongly effected on the development of the shipping industry. Building ships wouldn't be possible without mathematic calculations. The knowledge of mathematics can be applied to calculate courses, line of position and positions or while underway to estimate the economy of different kinds of cargo shipments and their stability during loading and discharging. Every vessel faces various kinds of weather conditions which can cause different movements like swinging. Aim of this paper is to explain the dynamic balance of swinging using mathematic equations. To understand this equation it is necessary to understand first "the swinging" as physical phenomenon and principle of solving mathematical equations to describe them