Geodesic
Brachistochrone with linear viscous friction
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2015), pp. 65-69 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A brachistochrone problem is considered for a medium with linear drag. The optimal control problem is reduced to a boundary value problem for a system of two nonlinear differential equations. The trajectories of this system are qualitatively analyzed, their typical features are found and verified by solving the boundary value problem numerically. 
@article{VMUMM_2015_3_a12,
     author = {A. V. Zarodnyuk and O. Yu. Cherkasov},
     title = {Brachistochrone with linear viscous friction},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {65--69},
     year = {2015},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2015_3_a12/}
}
TY  - JOUR
AU  - A. V. Zarodnyuk
AU  - O. Yu. Cherkasov
TI  - Brachistochrone with linear viscous friction
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2015
SP  - 65
EP  - 69
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2015_3_a12/
LA  - ru
ID  - VMUMM_2015_3_a12
ER  - 
%0 Journal Article
%A A. V. Zarodnyuk
%A O. Yu. Cherkasov
%T Brachistochrone with linear viscous friction
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2015
%P 65-69
%N 3
%U http://geodesic.mathdoc.fr/item/VMUMM_2015_3_a12/
%G ru
%F VMUMM_2015_3_a12
A. V. Zarodnyuk; O. Yu. Cherkasov. Brachistochrone with linear viscous friction. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2015), pp. 65-69. http://geodesic.mathdoc.fr/item/VMUMM_2015_3_a12/

[1] Ashby N., Britten W.E., Love W.F., Wyss W., “Brachistochrone with Coulomb friction”, Amer. J. Phys., 43:10 (1975), 902–905 | DOI | MR

[2] Lipp S.C., “Brachistochrone with Coulomb friction”, SIAM J. Control Optim., 35:2 (1997), 562–584 | DOI | MR | Zbl

[3] Negron-Marrero P.V., Santiago-Figueroa B.L., The Nonlinear Brachistochrone Problem with Friction, Technical Report PR 00791-4300, Department of Mathematics, University of Puerto Rico, Humacao, 2005

[4] Golubev Yu.F., “Brakhistokhrona s treniem”, Izv. RAN. Teoriya i sistemy upravleniya, 2010, no. 5, 41–52 | Zbl

[5] Abuladze M.V., “O passivnom polete na maksimalnuyu dalnost”, Vestn. Mosk. un-ta. Matem. Mekhan., 1986, no. 2, 102–105

[6] Pontryagin L.S., Boltyanskii V.G., Gamkrelidze R.V., Mischenko E.F., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1983 | MR