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

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.

electromagnetic interaction, electromagnetic radiation, flat–parallel motion, dynamic equations

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