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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, Volume 27, Number 3, Pages 115–127
DOI: https://doi.org/10.21538/0134-4889-2021-27-3-115-127 (Mi timm1842) 		 
On the Duality of Mathematical Models for Problems in Mechanics and in the Theory of Electrical Circuits

A. B. Kurzhanskia, A. A. Usovabc

a Lomonosov Moscow State University
b N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
c Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
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DOI: https://doi.org/10.21538/0134-4889-2021-27-3-115-127
Abstract: Considered in this paper are mathematical models of mechanics together with the theory of electrical circuits, and their similar dynamical structure is revealed. Using basic analogies, a chain of mechanical springs and an equivalent electrical analogue are constructed. Examples of “successful” borrowings are given, when methods of the theory of electrical circuits may be used to solve stabilization problems for a mechanical system formed by a set of interconnected mechanical subsystems.
Keywords: mechanical system, electrical circuit, duality of mechanical and electrical systems, stabilization of interconnected systems.
Funding agency Grant number
Russian Science Foundation 19-11-00105
This work was supported by the Russian Science Foundation (project no. 19-11-00105).
Received: 04.06.2021
Revised: 26.07.2021
Accepted: 09.08.2021
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2022, Volume 317, Issue 1, Pages S109–S120
DOI: https://doi.org/10.1134/S0081543822030099
Bibliographic databases:
Document Type: Article
UDC: 519.711.3
MSC: 93-02, 93D25, 93D15, 93C85
Language: Russian
Citation: A. B. Kurzhanski, A. A. Usova, “On the Duality of Mathematical Models for Problems in Mechanics and in the Theory of Electrical Circuits”, Trudy Inst. Mat. i Mekh. UrO RAN, 27, no. 3, 2021, 115–127; Proc. Steklov Inst. Math. (Suppl.), 317, suppl. 1 (2022), S109–S120
Citation in format AMSBIB
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\paper On the Duality of Mathematical Models for Problems in Mechanics and in the Theory of Electrical Circuits
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\yr 2021
\vol 27
\issue 3
\pages 115--127
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\jour Proc. Steklov Inst. Math. (Suppl.)
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