The perturbed point motion bringing to the base trajectory in the geometric constraints on additional controls presence

The deriving the perturbed material point motion in a small neighborhood of the base trajectory problem is solved in this paper. Assumed that geometric constraints in the form of convex compact sets are imposed on the additional controls. In particular, the cases of spheres, ellipsoids and rectangular parallelepipeds were considered. As a result of the constructed control, all the requirements for the kinematics of the point flight were satisfied: the point hitting prohibition with given regions and the necessity of its location in the given vertical strip above the ground surface. The numerical experiment confirmed the effectiveness of the proposed algorithm.