Far Eastern Mathematical Journal

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


Gladkov S.O., Bogdanova S.B.

2020, issue 1, Ń. 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

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References

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