Geodesic
Features of the support reaction in the range maximization problem in a resistant medium
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2018) no. 2, pp. 147-158

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{FPM_2018_22_2_a8,
     author = {A. V. Zarodnyuk and D. I. Bugrov and O. Yu. Cherkasov},
     title = {Features of the support reaction in the range maximization problem in a resistant medium},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {147--158},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2018_22_2_a8/}
}
TY  - JOUR
AU  - A. V. Zarodnyuk
AU  - D. I. Bugrov
AU  - O. Yu. Cherkasov
TI  - Features of the support reaction in the range maximization problem in a resistant medium
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2018
SP  - 147
EP  - 158
VL  - 22
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2018_22_2_a8/
LA  - ru
ID  - FPM_2018_22_2_a8
ER  - 
%0 Journal Article
%A A. V. Zarodnyuk
%A D. I. Bugrov
%A O. Yu. Cherkasov
%T Features of the support reaction in the range maximization problem in a resistant medium
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2018
%P 147-158
%V 22
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2018_22_2_a8/
%G ru
%F FPM_2018_22_2_a8
A. V. Zarodnyuk; D. I. Bugrov; O. Yu. Cherkasov. Features of the support reaction in the range maximization problem in a resistant medium. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2018) no. 2, pp. 147-158. http://geodesic.mathdoc.fr/item/FPM_2018_22_2_a8/