Vol 71, No 4 (2016)

The entry of a space body with a super orbital velocity into the Earth’s atmosphere is considered. Large aerodynamic loads, the forces of inertia, and the thermal flows to the body lead to the surface mass loss and to a possible mechanical failure. From observations it is known that the flight of a space body often ends with a powerful final burst. One of the adequate approaches to the estimation of energy release at the final stage of the body’s destruction is proposed to confirm the possibility of observing the effect of “thermal explosion” of a meteoroid.

The problem of maximizing the horizontal coordinate of a point moving in a vertical plane under the action of gravity and dry friction and the corresponding brachistochrone problem are considered. The optimal control problem is reduced to a boundary value problem for a system of two nonlinear differential equations. A qualitative analysis of the trajectories of this system is carried out, their typical features are found and illustrated by numerical solving of the boundary value problem. It is shown that the normal component of the support reaction should be positive when moving along the optimal curve. The optimality of the found extremals is discussed.