The present paper considers the general aspects and mathematical foundation of the subsystem of on-board universal pilot’s support system, which provides pilot’s control actions support during more or less long-term maneuvers, such as take-off and climbing, flight on a route, surface-based target attack (in case of military aircraft), descent and landing via shortcut-time on-board optimization of spatial trajectories and their head-up display visualization in the view of “road-in-the-sky” image for further tracking in “director with sight” regime or (semi) automatic mode. There are mentioned briefly the main ideas of two specially designed for this purpose “fast” modifications of the direct method of calculus of variations. One (for short-term trajectories with strong restrictions on controls) based on 5th-7th order polynomial approximation; the second (for flight on a route) based on spline approximation. Both from a conditional arc argument, with obligatory a priory satisfaction of boundary values of phase coordinates and controls and meeting all another restrictions in the process of optimization. Proposed algorithms were already implemented and tested on board of the real aircraft. So present paper contains some results of this flight test.