A qualitative analysis of the brachistochrone problem with dry friction and maximizing the horizontal range
- Authors: Zarodnyuk A.V.1, Cherkasov O.Y.1
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Affiliations:
- Faculty of Mechanics and Mathematics
- Issue: Vol 71, No 4 (2016)
- Pages: 93-97
- Section: Article
- URL: https://journals.rcsi.science/0027-1330/article/view/164372
- DOI: https://doi.org/10.3103/S002713301604004X
- ID: 164372
Cite item
Abstract
The problem of maximizing the horizontal coordinate of a point moving in a vertical plane under the action of gravity and dry friction and the corresponding brachistochrone problem are considered. The optimal control problem is reduced to a boundary value problem for a system of two nonlinear differential equations. A qualitative analysis of the trajectories of this system is carried out, their typical features are found and illustrated by numerical solving of the boundary value problem. It is shown that the normal component of the support reaction should be positive when moving along the optimal curve. The optimality of the found extremals is discussed.
About the authors
A. V. Zarodnyuk
Faculty of Mechanics and Mathematics
Author for correspondence.
Email: alenaz_90@inbox.ru
Russian Federation, Leninskie Gory, Moscow, 119899
O. Yu. Cherkasov
Faculty of Mechanics and Mathematics
Email: alenaz_90@inbox.ru
Russian Federation, Leninskie Gory, Moscow, 119899
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