Т.Ya. Shevgunov – Ph.D. (Eng.), Associate Professor, Moscow Aviation Institute (National Research University) E-mail: shevgunov@gmail.com
Е.N. Efimov – Ph.D. (Eng.), Research Scientist, Moscow Aviation Institute (National Research University) E-mail: omegatype@gmail.com
In this paper, the application of Lagrangian mechanic principles is introduced for dynamic analysis of lumped-element electric circuits containing resistors and sources of independent voltages and currents. It was discussed that formal analogy between the generalized coordinates of masses in classical mechanics and charges in electric circuit theory allows making up a clear qualitative interpretation of the proposed analytical method that paves the way for its further application to analysis of complex physical systems.
- Lagranzh Zh.L. Analiticheskaya mehanika. M.-L.: GITTL. 1950.
- Sudakov V.F. Kanonicheskie uravneniya dlya konservativnyh cepej c dvumya stepenyami svobody // Vestnik MGTU im. N.E. Baumana. Ser. «Priborostroenie». 2014. № 1. S. 58–69.
- Clemente-Gallardo J., Scherpen J.M.A. Relating Lagrangian and Hamiltonian formalisms of LC circuits // IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications. 2003. V. 50. № 10. P. 1359–1363. Doi: 10.1109/TCSI.2003.817781.
- Ober-Blöbaum S., Tao M., Cheng M., Owhadi H., Marsden J.E. Variational integrators for electric circuit // Journal of Computational Physics. 2013. V. 242. P. 498–530. Doi:10.1016/j.jcp.2013.02.006.
- Özdaş K., Kiliçkaya M.S. Novel method for the analysis of RLC circuits // International journal of electronics theoretical and experimental. 1991. 70:2. P. 407–412. Doi: 10.1080/00207219108921288.
- Kadhim Y. Lagrangian description of electric circuits // Lecture Notes. Course Code: FYGB08. Karlstad University. Faculty of health, science and technology. Department of Engineering and Physics. P. 1–8.
- El'sgol'c L. Variacionnoe ischislenie. M. URSS. 2014.
- Medvedev B.V. Nachala teoreticheskoj fiziki. Mehanika, teoriya polya, elementy kvantovoj mehaniki. M.: Fizmatlit. 2007. S. 19–23.
- Mayer D. Hamilton’s Principle and Electric Circuits Theory // Advances in Electrical and Electronic Engineering. 2006. P. 185–189.
- Baskakov S.I. Lekcii po teorii cepej. URSS. 2016.
- Lindell I.V. Heaviside operational rules applicable to electromagnetic problems // Progress in electromagnetics research. PIER 26. 2000. P. 293–331.
- Batchelor G.K. An Introduction to Fluid Dynamics. Cambridge Mathematical Library series. Cambridge University Press. 2000.