Computational modeling has become a prominent tool to simulate physical processes for research and development projects. The coastal region of southern Brazil is very susceptible to oil spill accidents. Currently, oil is intensively transported in the region due to the presence of the Rio Grande Harbor, the Transpetro Waterway Terminal (Petrobras) and the Riograndense S/A Oil Refinery. Therefore, simulations under ideal navigation conditions for ships with potentially polluting loads are important because their use can reduce oil spills and toxic compound accidents in the environment. Therefore, the main objective of this work is to present a preliminary study of the contribution of external forces to a ship’s behavior over a simulation period of 5 h. The methodology is based on the development of a numerical model using LaGrangian formalism and the calculus of variations, besides Maneuvering Modeling Group (MMG Model). The external forces considered were the wind acting directly on the ship, waves driven by wind, the rudder, the force acting on the hull, inertial forces, and seawater density. The results indicate that at the beginning of the simulation, the inertial forces were of primary importance for controlling the trajectory of the ship. After 5 h of simulations, the ship had completely changed its trajectory due to forces suffered by the ship, classified according to MMG Model.