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Banshchikov A. V., Vetrov A. A., Irtegov V. D., Titorenko T. N. Analiz elektricheskikh tsepei sredstvami komp'yuternoi algebry v mashinovedenii [Analysis of electrical circuits by means of computer algebra in machine science]. Sovremennye tekhnologii. Sistemnyi analiz. Modelirovanie [Modern Technologies. System Analysis. Modeling], 2018, Vol. 60, No. 4, pp. 46–54. DOI: 10.26731/1813-9108.2018.4(60).46-54

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Electrical circuits have long been diversely applied in transport and other fields of engineering. The paper presents an original model and, based on it, a visual editor of the electrical circuit graph developed in the integrated environment of Embarcadero Delphi in Object Pascal language. The novelty of the approach is that the basic information about the graph is expanded by data on the parameters and functions of the circuit diagram for the automatic generation of its symbolic description. Through graphical user interface for a specific nonlinear electrical circuit, a graph and a corresponding description in the form of a nested list are formed for further investi-gation by previously created software complexes for modeling and qualitative analysis of electrical circuits in symbolic form on PC. A dynamic analysis was carried out for the investigated chain: namely, a symbolic model (mixed potential and differential equations of state) was constructed, certain equilibrium positions (time-independent solutions of the state equations) were found and the question of their Lyapunov stability by means of the outlined equations of perturbed motion in the first approximation. The conditions for the as-ymptotic stability in the form of a system of Lienard-Chipard inequalities are obtained in terms of the coefficients of the characteristic polynomial of sixth degree. During the parametric analysis of stability conditions, the programming language tools and the functions of symbolic-numerical modeling of the computer algebra system “Mathematica” were used. A graphic interpretation of the results of the study on the equilibrium positions stability is presented


Работа выполнена при финансовой поддержке Российского фонда фундаментальных исследований, грант № 16-07-00201a.

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