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Dal'nevost. Mat. Zh., 2020, Volume 20, Number 1, Pages 15–37 (Mi dvmg416)  

To the theory of synchronization of interacting pendulums oscillating in the parallel planes

S. O. Gladkov, S. B. Bogdanova

Moscow Aviation Institute (National Research University)

Abstract: The problem of interacting metal pendulums oscillating in parallel planes, the distance $b$ between the suspension points of which is fixed and equally, has been solved. The principle possibility of their synchronization is provided by taking into account two physical factors: 1. Effect of electromagnetic interaction between them and 2. Accounting for EM radiation of each pendulum, leading to non-linear attenuation. The system of nonlinear dynamic motion equations obtained by a strict mathematical path is analyzed, and their numerical solution is given. The article offers a new method for constructing the pairs of function which are holomorphic on the whole complex plane and satisfy functional equations such as the addition theorem for theta functions.

Key words: electromagnetic interaction, electromagnetic radiation, flat – parallel motion, dynamic equations.

DOI: https://doi.org/10.47910/FEMJ202003

Full text: PDF file (475 kB)
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UDC: 531.36+534.1
MSC: 37H99
Received: 12.09.2019

Citation: S. O. Gladkov, S. B. Bogdanova, “To the theory of synchronization of interacting pendulums oscillating in the parallel planes”, Dal'nevost. Mat. Zh., 20:1 (2020), 15–37

Citation in format AMSBIB
\Bibitem{GlaBog20}
\by S.~O.~Gladkov, S.~B.~Bogdanova
\paper To the theory of synchronization of interacting pendulums oscillating in the parallel planes
\jour Dal'nevost. Mat. Zh.
\yr 2020
\vol 20
\issue 1
\pages 15--37
\mathnet{http://mi.mathnet.ru/dvmg416}
\crossref{https://doi.org/10.47910/FEMJ202003}


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