Nonstandard analysis in electrical engineering. The analysis of the direct current circles with ideal reactive elements.

Abstract

The article proposes the use of ideas and methods of non-standard analysis in the field of theoretical electronics. The article shows that the analysis of DC circuits, including ideal inductances and capacitances, by standard methods of theoretical electrical engineering is too complicated or almost impossible. To solve this problem, it is proposed to extend the methods of non-standard analysis by the tasks of analyzing electrical circuits with ideal reactive elements. The authors have defined a class of non-standard electrotechnical problems aimed at the analysis of DC electrical circuits, including ideal reactive elements — ideal inductances and capacitances. It is shown that the solution of the selected class of problems by standard methods of theoretical electrical engineering is too difficult or almost impossible. It is proposed to extend the methods of non-standard analysis by the tasks of analyzing electrical circuits with ideal reactive elements. The obtained advantages of this approach are confirmed by examples of calculations of electrical circuits with inductances and capacitances, as well as magnetic circuits.