MATHEMATICAL MODELS OF SOME PROBLEMS OF SHIPPING AND HYDRAULIC ENGINEERING CONSTRUCTION

Abstract

The processes taking place in the global economy, including rising energy prices and environmental issues, are intensifying the search for the most efficient ways to deliver goods. In this sense, maritime transport has many advantages and is very promising. In the shipping industry, the task of optimizing routes to minimize transportation costs and reduce the time for cargo delivery is a pressing one. Equally important in this regard are the problems of water resources management, port construction and waterways, construction of coastal, port and marine hydraulic structures. The main tasks of hydraulic engineering construction are to increase the strength of structures and optimize the cost of their construction. Mathematical methods and models play a leading role in engineering research. Building a mathematical model involves identifying the main factors of the process under study (selecting its parameters and characteristics) and determining the relationship between them. The creation of a mathematical model is completed by writing these relationships in an analytical form. The resulting objective function, together with additional conditions (equations and inequalities), is investigated by methods of mathematical analysis, in particular the theory of differential equations. An important stage in solving the problem is the analysis of the results. The paper considers some problems of hydraulic engineering construction: the problem of water pressure on a dam or a sluice and the problem of the location of groundwater in the drainage system. The paper also considers problems related to the movement and maneuvering of ships, in particular, the problem of searching for a submarine using a marine drone, the problem of the movement of two ships relative to each other. The ship pitching problem is one of the questions of ship theory. For each of these problems, a corresponding mathematical model was created and studied. The consideration of these problems in a higher mathematics course contributes to a better understanding of the connection between mathematical theory and practice and its importance in the study of physical processes and engineering.