Geodesic
Principle of energies of partial motions for mechanical, electrical and electromechanical holonomic systems with multiple degrees of freedom
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 74 (2021), pp. 127-140 Cet article a éte moissonné depuis la source Math-Net.Ru

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The purpose of this research is to formulate and prove the principle of energy of partial subsystems for mechanical, electrical, and electromechanical holonomic systems with time-independent constraints, as well as the development of a simple method to derive equations of motion for such systems. This principle is helpful in giving short courses of theoretical mechanics to students who know only the basic principle of energy and the D'Alembert principle. Two issues are covered in this paper: firstly, the formulation of the principle of energies for interacting mechanical partial subsystems, including the proof of the theorem, and, finally, the application of the developed method for mechanical, electrical, and electromechanical systems. The energy principle is developed using the D'Alembert principle for partial motions of the system when deriving kinetic and power balance equations. For electrical and electromechanical systems, the principle is based on the first electromechanical analogy of Maxwell's postulate and Kirchhoff 's laws. As examples, the principle allowed obtaining equations of motion of mechanical systems with three degrees of freedom: rotation of a disk on an elastic shaft, dynamics of a vibration table, an electrical system with two cyclic currents connected through a resistor, and an electromechanical system of the acceleration sensor.
Keywords: equations of motion for systems with multiple degrees of freedom, D'Alembert's principle, partial motions and their equations, power equations, partial and external inertial forces, Kirchhoffs second law, electromechanical analogy, principle of energies of partial motions for mechanical, electrical and electromechanical systems, examples. 
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     author = {A. I. Rodionov and S. R. Kravtsov},
     title = {Principle of energies of partial motions for mechanical, electrical and electromechanical holonomic systems with multiple degrees of freedom},
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A. I. Rodionov; S. R. Kravtsov. Principle of energies of partial motions for mechanical, electrical and electromechanical holonomic systems with multiple degrees of freedom. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 74 (2021), pp. 127-140. http://geodesic.mathdoc.fr/item/VTGU_2021_74_a12/

[1] Gantmakher F.R., Lektsii po analiticheskoi mekhanike, ucheb. posobie dlya vuzov, 3-e izd., ed. E.S. Pyatnitskii, Fizmatlit, M., 2001, 264 pp.

[2] Butenin N.V., Fufaev N.A., Vvedenie v analiticheskuyu mekhaniku, 2-e izd., per. i dop., Nauka, M., 2014, 256 pp. | MR

[3] V.I. Drong, V.V. Dubinin, M.M. Ilin i dr., Kurs teoreticheskoi mekhaniki, uchebnik dlya vuzov, ed. K.S. Kolesnikov, Izd-vo MGTU im N.E. Baumana, M., 2000, 736 pp.

[4] Rodionov A.I., Kim V.F., Teoreticheskaya mekhanika: konspekt lektsii s prilozheniyami, v. 3, Dinamika, Izd-vo NGTU, Novosibirsk, 2010, 240 pp.

[5] Nolting W., Theoretical Physics, v. 2, Analytical Mechanics, Springer International Publishing, Switzerland, 2016 | DOI

[6] Lemos N.A., Analytical Mechanics, Cambridge University Printing House, United Kingdom, 2018 | DOI | MR | Zbl

[7] Ostromenskii P.I., Rodionov A.I., “Sostavlenie i issledovanie differentsialnykh uravnenii dvizheniya mekhanicheskikh sistem metodom obobschennykh sil”, Nauchnyi vestnik NGTU, 1997, no. 1(3), 121–140

[8] Ostromenskii P.I., “Issledovanie dinamiki mashin metodom dinamicheskikh reaktsii”, Voprosy dinamiki mekhanicheskikh sistem, Novosibirskii elektrotekhnicheskii institut, Novosibirsk, 1983, 36–44

[9] Usoltsev A.A., Obschaya elektrotekhnika, uchebnoe posobie, SPbGU ITMO, SPb, 2009, 301 pp.

[10] Zhulovyan V.V., Osnovy elektromekhanicheskogo preobrazovaniya energii, uchebnik, Izd-vo NGTU, Novosibirsk, 2014, 427 pp.

[11] Zelenkov A.A., Theory of Electrical Engineering. Electric Circuits with the Distributed Parameters. Theory of Electromagnetic Field: a Textbook, NAU, Kyiv, 2012