Benefits of using matrix methods in teach-ing mechanics in higher education institu-tions

Abstract

Problem. Basic concepts, concepts, principles of mechanics are mainly taught from simple to complex in institutions of higher technical education, which to some extent resembles a course on the history of mechanics. In today's conditions, the education system is required to take into account current trends in scientific and engineering fields. The use of inherently geometric methods of vector algebra and vector analysis as a basis for studying mechanics is losing its relevance. To a certain extent, this approach interferes with the use of multidimensional spaces (configurational and phase), tensor algebra, and computer technologies in modeling complex mechanical systems. Goal. The goal is to expand the field of application of the matrix formalism to infinite-dimensional spaces, justify its advantages compared to other approaches used in teaching the basics of mechanical disciplines, and demonstrate its capabilities in solving complex practical problems, both in terms of modeling and in terms of using computer technologies. Methodology. The methodological basis for choosing matrix methods is the use of infinite-dimensional and abstract, in physical terms, spaces when studying the movement of mechanical systems. The fundamental impossibility of accurately describing the state of a mechanical system requires the use of statistical modeling methods and the extension of the so-called law of conservation of matter in the form of a balance equation to these models. Results. It is shown that the matrix method, which is widely used in quantum mechanics and very limited in classical mechanics, allows you to use the advantages of the transition to phase space when obtaining canonical equations and when solving problems of kinematics and dynamics of a solid body. Originality. The paper proposes certain improvements of the matrix apparatus, related to the use of geometric parameters of the mechanical system as indexes. That is, infinite-dimensional matrices with real coefficients are used. Practical value. The proposed method allows you to effectively solve the problems of the mechanics of an absolutely rigid body without using any theorems of the general course, remaining within the limits of standard mathematical training.