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About tautochronic movements
- Authors: Petrov A.G.1
-
Affiliations:
- Ishlinsky Institute of Mechanics Problems of RAS
- Issue: Vol 518, No 1 (2024)
- Pages: 22-28
- Section: MATHEMATICS
- URL: https://journals.rcsi.science/2686-9543/article/view/269372
- DOI: https://doi.org/10.31857/S2686954324040045
- EDN: https://elibrary.ru/YZNYQS
- ID: 269372
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Abstract
It is shown that a material point, under the influence of an attractive linear force and a repulsive force inversely proportional to the cube of the distance from the center of attraction, performs a periodic motion, the period of which does not depend on the initial data (tautochronic motion). The problem is reduced to a nonlinear autonomous second-order equation, the general solution of which is expressed in terms of elementary functions. It has also been proven that for other power laws of repulsive force, except for degrees 0, 1 and –3, the movement of a material point is not tautochronous.
About the authors
A. G. Petrov
Ishlinsky Institute of Mechanics Problems of RAS
Author for correspondence.
Email: petrovipmech@gmail.com
Russian Federation, Moscow
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