Abstract
In the process of studying mathematics, it is important to show the application of its results in other disciplines. The use of mathematics in the study of special disciplines can be carried out in the process of interdisciplinary connections, as well as in solving applied problems. In various applications, particularly in analytical mechanics, it is possible to use certain provisions of the theory of differential games, namely, the conditions for the existence of equilibrium situations in non-cooperative differential games of several persons. This article presents studies of the necessary conditions for the existence of an equilibrium situation, using some concepts and principles of analytical mechanics. Thus, to define the action according to Hamilton, the necessary conditions were obtained in the form of the Euler-Lagrange equations. This form of necessary conditions in N-person differential games is of interest to students of natural sciences.