Flight Range Maximization Problem for a Simplified Aircraft Model

The flight range maximization problem for a simplified aircraft model, taking into account the influence of the amount of fuel on the dynamics of the center of mass, is considered. It is assumed that the motion occurs in a vertical plane under the influence of homogeneous gravity forces and homogeneous resistance of the medium. In addition, there is an active thrust force, as well as the ability to change the angle of inclination of the trajectory. These parameters are accepted as controls. An area in the space of initial variables is constructed for which the problem of optimal synthesis is solved. It is shown that in this area the thrust can take the maximum, zero, or singular value. The number and consequence of the trajectory arcs with the corresponding thrust are established.