Abstract:
In 21st century economically feasible and less expensive ways of space exploration and
industrialization become the great challenge for mankind. One of the promising approaches is development of
modern SSTO (single-stage-to-orbit) and VTOL (vertical-take-off-landing) technologies, leveraging latest
achievements in new materials and propulsion systems. The paper presents results of simulation of dynamic
systems, moving in central gravitational field, in an environment, where atmospheric drag force has a serious
impact on system’s dynamics. Model, proposed in paper, has been analyzed and build, based on Pontrjagin’s
principle of optimality. Optimal regular and singular thrust control of engine is analyzed. Research has been
conducted on relations between optimal control feasibility and SSTO parameters, including initial acceleration
and average (along trajectory) drag coefficient. Impact of drag dependence on Mach number on accuracy of
computed optimal trajectory has been considered. One approach to solve the problem has been developed, where
impact of proposed optimal control implementation on problem’s optimality criteria is evaluated. The derived
formula for calculating optimal control is invariant to conditions on right end of ascent trajectory.
