Аннотация:The problem of maximization of the horizontal coordinate and minimization of the fuel
expenditures of mass-point moving in the vertical plane driven by gravity, linear and quadratic viscous
drag, and thrust is considered. The slope angle and the thrust are considered as a control variables. The
problem is related to the modified brachistochrone problem. 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. Thrust control depending on the velocity and slope angle is designed. It is
established that the extreme thrust control program consists either of single arc with intermediate thrust
control, or two arcs, starting with maximum thrust and ending with the intermediate thrust or three arcs:
”intermediate-maximum-intermediate”.