Abstract
The problem of maximization of the horizontal range and minimization of time for a point mass moving in a resisting medium is analyzed. Various models of medium resistance are considered. Using Pontryagin's maximum principle, the optimal control problem is reduced to the boundary value problem for a system of two nonlinear differential equations. The qualitative analysis of the resulting system makes it possible to reveal previously unknown characteristics of optimal trajectories for a general model of the resistance force. This analysis is illustrated by a numerical simulation.
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