DEVELOPMENT OF MATHEMATICAL MODELS FOR DESIGNING EDUCATIONAL RESOURCES IN HIGHER SCHOOL
Authors:   Vinnytsya National Agrarian University, Dubchak Viktor 
Published: February 2024

Purpose. An urgent issue in many branches of the modern economy is the possibility of various uses of large-volume containers of various manufacturing geometries for the purpose of storage, transportation and use of various types of technical liquids, water, etc. The most common geometry for the manufacture of such containers is cylindrical, hemispherical, parabolic tanks. In most cases, the spatial arrangement of such containers during their direct use has a vertical orientation. But as the review and trends of modern uses of such cylindrical structures show, there is a trend towards their horizontal or combined location methods during practical operation. The volume of the filler in the conditions of constant use of such containers is also constantly changing, and therefore the main energy characteristics of the filler materials themselves change accordingly, to which we can attribute the volume of liquid, the set of static moments, as a result, the coordinates of the center of gravity, the moments of inertia relative to those or other coordinate axes, planes, etc. The issue of changing certain geometric characteristics when changing the location of such cylindrical containers from horizontal to vertical or vice versa can be interesting and relevant. A significant number of sectors of the economy show interest in plastic horizontal containers for water storage, and this is understandable, because the ease of use and variety of products attract an increasing number of consumers. Plastic types of cylindrical containers have been gaining popularity in various industries for a long time due to their useful features. Innovative technologies and materials have made it possible to create plastic products of various shapes, sizes and purposes, and this has many obvious advantages. The use of plastic materials in the manufacture of various containers allows you to significantly reduce the initial weight of such a product in comparison with its metal counterparts or glass products, which means that when establishing the main energy characteristics, the weight of the container itself can be neglected. In addition, the use of this type of container is convenient for its transportation, installation, etc.The results of scientific analytical studies are also presented, which ensure the determination of the pressure force on underwater hydroelectric structures, such as, for example, dams of hydroelectric power plants, liquid organic fertilizer and wastewater sedimentation tanks, coastal fortifications of lakes, rivers, ponds, reservoirs, etc.The practical experience of industrial and pedagogical activities and the analysis of inventive and research works of domestic and foreign scientists have shown that the structural, technological and economic feasibility, operational safety of underwater hydraulic structures requires further analytical and computational studies based on mathematical optimization methods. The achievements of Chinese scientists are of particular great scientific interest. Their achievements in the calculation, design, construction and operation of small and large hydroelectric power plants are recognized by scientists, designers and manufacturers in the world.The work is based on research aimed at the mathematical substantiation of the parameters of a rectangular, trapezoidal lock and a circular hatch, which is located at an arbitrary, optimally structurally justified depth.It is taken into account that every year new students are enrolled in universities who need to acquire knowledge on the calculation of the strength of structures of objects with the involvement of innovative methods based on fundamental mathematical apparatus. The formation of the professional competences of a modern agricultural engineer should ensure the ability to apply the theoretical foundations and basic methods of physics and mathematics, hydrostatics, dynamics, fluid mechanics for the calculation and design of technical objects and, of course, underwater hydraulic structures. An agricultural engineer must be able to perform calculations on the strength of the walls of containers of any geometric profiles for storing liquids, as well as the side walls and bottoms of hydraulic structures, bodies that are placed in liquids.The work also presents and investigates calculations of volumes in the form of geometric shapes of containers of a standard shape, such as a cone, sphere, and cylinder, using curvilinear coordinates, including cylindrical and spherical ones. The comparative method of calculating a specific mathematical characteristic, namely volume, confirms the effectiveness of using cylindrical coordinates in the case of separation of one of the independent variables, and spherical coordinates, if all three variables describing the corresponding surface are equal.