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Fundamentalnaya i Prikladnaya Matematika, 2018, Volume 22, Issue 2, Pages 147–158 (Mi fpm1793)  

Features of the support reaction in the range maximization problem in a resistant medium

A. V. Zarodnyuk, D. I. Bugrov, O. Yu. Cherkasov

Lomonosov Moscow State University, Moscow, Russia
References:
Abstract: The horizontal coordinate's maximization problem of a mass-point as well as the corresponding brachistochrone problem is considered. The mass-point is supposed to be moving in a vertical plane under the influence of gravity and viscous drag that is proportional to the $n$th degree of the velocity. The analysis of the reaction force, which is considered as control along the extremal curve, is provided. It is established that the reaction of the basement can change its sign no more than one time, moreover, it changes only from negative values to positive values.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00538_а
17-08-01366_а
This work was supported by RFBR according to the research project No. 18-01-00538 (reaction’s sign depending on the resistance law) and project No. 17-08-01366 (reaction’s sign depending on the velocity).
English version:
Journal of Mathematical Sciences (New York), 2021, Volume 253, Issue 6, Pages 858–866
DOI: https://doi.org/10.1007/s10958-021-05275-9
Document Type: Article
UDC: 531.552
Language: Russian
Citation: A. V. Zarodnyuk, D. I. Bugrov, O. Yu. Cherkasov, “Features of the support reaction in the range maximization problem in a resistant medium”, Fundam. Prikl. Mat., 22:2 (2018), 147–158; J. Math. Sci., 253:6 (2021), 858–866
Citation in format AMSBIB
\Bibitem{ZarBugChe18}
\by A.~V.~Zarodnyuk, D.~I.~Bugrov, O.~Yu.~Cherkasov
\paper Features of the support reaction in the range maximization problem in a resistant medium
\jour Fundam. Prikl. Mat.
\yr 2018
\vol 22
\issue 2
\pages 147--158
\mathnet{http://mi.mathnet.ru/fpm1793}
\transl
\jour J. Math. Sci.
\yr 2021
\vol 253
\issue 6
\pages 858--866
\crossref{https://doi.org/10.1007/s10958-021-05275-9}
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    Фундаментальная и прикладная математика
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