Geodesic
To the theory of synchronization of interacting pendulums oscillating in the parallel planes
Dalʹnevostočnyj matematičeskij žurnal, Tome 20 (2020) no. 1, pp. 15-37 
S. O. Gladkov; S. B. Bogdanova. To the theory of synchronization of interacting pendulums oscillating in the parallel planes. Dalʹnevostočnyj matematičeskij žurnal, Tome 20 (2020) no. 1, pp. 15-37. http://geodesic.mathdoc.fr/item/DVMG_2020_20_1_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] S. O. Gladkov, S. B. Bogdanova, “Khaoticheskaya dinamika vzaimodeistvuyuschikh mayatnikov (reshenie problemy sinkhronizatsii)”, Inzhenernaya fizika, 2019, no. 1, 49–62

[2] S. O. Gladkov, S. B. Bogdanova, “Teoriya determinirovannogo khaosa v sisteme N vzaimodeistvuyuschikh komplanarnykh mayatnikov”, Inzhenernaya fizika, 2019, no. 3, 9–21

[3] Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence, Berlin, 1984 | DOI | MR

[4] S. O. Gladkov, “K teorii raspredeleniya EM polei dlya potentsialov Lienara – Vikherta”, Inzhenernaya fizika, 2018, no. 8, 3–10

[5] L. Landau, E. Lifshits, Teoriya polya, Nauka, M., 2001

[6] L. Landau, E. Lifshits, Elektrodinamika sploshnykh sred, Nauka, M., 2002 | MR

[7] S. O. Gladkov, “K voprosu o vychislenii vremeni ostanovki vraschayuschegosya v vyazkom kontinuume tsilindricheskogo tela i vremeni uvlecheniya soosnogo s nim vneshnego tsilindra”, ZhTF, 59:3 (2018), 377–341

[8] A. Andronov, A. Vitt, S. Khaikin, Teoriya kolebanii, Fizmatlit, M., 1959

[9] S. O. Gladkov, “On the Possibility of Detecting Different Kinds of Diseases with the Help of Fixation of Electromagnetic Radiation Intensity of Red Blood Cells”, Biomedical Journal Scientific and Technical Research, 20 (1) (2019), 14806-14808