INFORMATION GRAPHIC TECHNOLOGIES IN MODELLING MULTIPARAMETER SYSTEMS

Abstract

When designing multiparameter technical systems, it is important to choose the design parameters by studying the course of processes involving multidimensional phase and state spaces. The formation of operational characteristics of the studied system is often performed using integrated curves or phase trajectories The results of visualization, interpretation and analysis of transients in technical systems are often justified by the use of second-order surfaces, in particular, cylindrical. Given the multiparameter system, it is important to establish the features of the projection images of such surfaces. The above gives grounds to consider the task of developing geometric means of mapping second-order surfaces in models of multiparameter technical systems using multidimensional Euclidean spaces, the measurability of which is determined by the number of functional parameters of the studied technical system. The construction of geometric images as manifolds and hypersurfaces of enveloping Euclidean spaces is traced in works on parameterization of multidimensional geometric images, in the development of a compositional method of surface formation by geometric means Balyuba–Najdysh calculus. Some works substantiate and generalize the geometric means of the phase plane to a multidimensional phase space. In applied multidimensional geometry, a limited number of scientific investigations are known to generalize the projections of the surfaces of three-dimensional Euclidean space. The purpose of the article is to study and substantiate the projection images of multidimensional cylindrical surfaces to expand the possibilities of practical application of geometric means of multidimensional phase and state spaces of technical systems.The graphical tools of applied multidimensional geometry for generalization of surfaces of the second order of threedimensional Euclidean space are considered by the example of cylindrical surfaces as means of researching multiparameter technical systems using their models. The features of projection images of three-dimensional cylindrical surfaces of four-dimensional Euclidean space are shown, taking into account the belonging of lowdimensional manifolds.