Conclusion of a heavy material point to the base trajectory subject to geometric constraints on additional controls

The article solves the problem of correcting controlled flight of a point moving in a uniform gravity field and experiencing resistance proportional to the square of the speed. Correction is carried out by introducing additional control, which imposes geometric restrictions in the form of a convex compact set. Under the assumption that the reachable region of the auxiliary linear dynamic object contains the origin, the fast-action problem was solved by deriving the corrected motion to the base trajectory.