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 Fundam. Prikl. Mat., 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

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_à17-08-01366_à

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UDC: 531.552

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

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}