ИСТИНА

Abstract. Motion of the material point in vertical plane is considered under assumption, that gravitational field and atmosphere are homogeneous. The problem is to determine the shape of the trajectory, ensuring the maximum horizontal distance from initial position for fixed time interval. Problem formulated above is close to the famous brachistohrone problem with friction. Maximum Principle is applied to reduce optimal problem to the boundary-value problem for the system of two nonlinear differential equations. Qualitative analysis of this system allows to determine typical features of the optimal trajectories.