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Equations of Motion for Bodies of the Same Mass Uniformly Distributed Over a Circle with Regard for the Speed of Gravity

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We study the problem of motion of an arbitrary finite set of points of the same mass uniformly distributed over a circle located on a fixed plane with regard for the speed of gravity. The center of the circle with an arbitrary given mass is regarded as fixed, and the initial state of points is such that, at all times, the points are located on a circle with time-dependent radius. It is shown that the motion of the studied system of points is described by a system of equations with delays. The investigation is reduced to the analysis of a single equation

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Authors and Affiliations

  1. National University of Water Management and Nature Resources Use, Soborna Str., 11, Rivne, 33000, Ukraine

    V. Yu. Slyusarchuk

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  1. V. Yu. Slyusarchuk
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Correspondence to V. Yu. Slyusarchuk.

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Translated from Neliniini Kolyvannya, Vol. 25, No. 4, pp. 404–412, October–December, 2022.

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Slyusarchuk, V.Y. Equations of Motion for Bodies of the Same Mass Uniformly Distributed Over a Circle with Regard for the Speed of Gravity. J Math Sci 277, 329–337 (2023). https://doi.org/10.1007/s10958-023-06836-w

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