Brachistochrone problem with linear viscous friction / A. V. Zarodnyuk, O. Yu. Cherkasov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2015. № 3. P. 65-69 [Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 70-74].
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.
Key words: brachistochrone problem, linear drag, optimal control, phase portrait.