Аннотация:The brachistochrone problem with penalty for fuel expenditures of masspoint
moving in the vertical plane driven by gravity, nonlinear viscous drag, and thrust
is considered. The lifting force or normal component of the reaction force of the curve
and the thrust are considered as a control variables. Principle maximum procedure allows
to reduce the optimal control problem to the boundary value problem for a set of
systems of two nonlinear differential equations. The qualitative analysis of the resulting
system allows to study the key features of the extremal trajectories, including asymptotic
behavior. Thrust control depending on the velocity and slope angle is designed.
The structure of the extremal thrust control program is determined and consequence of
the subarcs is established analytically