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On the Duality of Mathematical Models for Problems in Mechanics and in the Theory of Electrical Circuits

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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.

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Funding

This work was supported by the Russian Science Foundation (project no. 19-11-00105).

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, 119991, Moscow, Russia

    A. B. Kurzhanski

  2. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 620108, Yekaterinburg, Russia

    A. A. Usova

  3. Ural Federal University, 620000, Yekaterinburg, Russia

    A. A. Usova

Authors
  1. A. B. Kurzhanski
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  2. A. A. Usova
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Correspondence to A. B. Kurzhanski or A. A. Usova.

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The author declares that he has no conflicts of interest.

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Translated from Trudy Instituta Matematiki i Mekhaniki UrO RAN, Vol. 27, No. 3, pp. 115 - 127, 2021 https://doi.org/10.21538/0134-4889-2021-27-3-115-127.

Translated by E. Vasil’eva

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Kurzhanski, A.B., Usova, A.A. On the Duality of Mathematical Models for Problems in Mechanics and in the Theory of Electrical Circuits. Proc. Steklov Inst. Math. 317 (Suppl 1), S109–S120 (2022). https://doi.org/10.1134/S0081543822030099

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