FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
To the theory of synchronization of interacting pendulums oscillating in the parallel planes |
Gladkov S.O., Bogdanova S.B. |
2020, issue 1, P. 15–37 DOI: https://doi.org/10.47910/FEMJ202003 |
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. |
Keywords: electromagnetic interaction, electromagnetic radiation, flat–parallel motion, dynamic equations |
Download the article (PDF-file) |
References |
| [1] S. O. Gladkov, S. B. Bogdanova, “Khaoticheskaia dinamika vzaimodeistvuiushchikh maiatnikov (reshenie problemy sinkhronizatsii)”, Inzhenernaia fizika, 2019, № 1, 49–62. [2] S. O. Gladkov, S. B. Bogdanova, “Teoriia determinirovannogo khaosa v sisteme N vzaimodeistvuiushchikh komplanarnykh maiatnikov”, Inzhenernaia fizika, 2019, № 3, 9–21. [3] Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence, Berlin, 1984. [4] S.O. Gladkov, “K teorii raspredeleniia EM polei dlia potentsialov Lienara – Vikherta” , Inzhenernaia fizika, 2018, № 8, 3–10. [5] L. Landau, E. Lifshits, Teoriia polia, Nauka, M., 2001. [6] L. Landau, E. Lifshits, Elektrodinamika sploshnykh sred, Nauka, M., 2002. [7] S.O. Gladkov, “K voprosu o vychislenii vremeni ostanovki vrashchaiushchegosia v viazkom kontinuume tsilindricheskogo tela i vremeni uvlecheniia soosnogo s nim vneshnego tsilindra” , ZhTF, 59:3, (2018), 377–341. [8] A. Andronov, A. Vitt, S. Khaikin, Teoriia 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. |