THE MAIN HAMILTON FUNCTION AND THE NECESSARY CONDITIONS FOR THE EXISTENCE OF A SITUATION IN THE FORM OF THE HAMILTON-JACOBI EQUATIONS - Makhmudova Ш.Д.; Urazgalieva А.Н. (Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences, 2021)
Interdisciplinary application of learning outcomes is essential to the field of mathematics, attainable at intersection of math with other subjects – which includes applied tasks When studying a number of technical disciplines, as well as solving applied problems, it is possible to use certain aspects of the theory of optimal control - which is an example of interdisciplinary link. Analytical mechanics, among other disciplines, enables leverage of certain aspects of the theory of differential games, namely, equilibrium conditions in non-coalitional differential games of several players. This article provides studies of the necessary and sufficient conditions for the existence of equilibrium situations, using some concepts of analytical mechanics. In line with Hamilton’s definition, necessary conditions were obtained in the form of Hamilton-Jacobi equations. This form of necessary conditions in differential games of N persons is of interest to students of natural and technical fields. The main goal of the article is to demonstrate interdisciplinary link, an important component of the process of training future engineers for various sectors of the economy. It is necessary for the holistic understanding of the material, so that students of technical specialties of various fields can use it. Proposed work can aid in study of this area of analytical mechanics by university students and young scientists alike.