Geodesic
Brachistochrone with linear viscous friction
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2015), pp. 65-69

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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},
     publisher = {mathdoc},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2015_3_a12/}
}
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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/