Open AccessEconomical space transportation systems to launch small satellites into Earth’s orbits are researched in many countries. Using aerospace systems, included aircraft and air-launched launch vehicle, is one of the low cost technical solutions. The airborne launch vehicle application to launch a small satellite with the purpose of remote sensing requires high precision exit on specified sun-synchronous orbit. So a problem is stated to construct an optimal ascent trajectory and optimal control.
In this paper, the mathematical motion model of the air-launched launch vehicle with the external disturbances caused by the Earth’s non-sphericity, drag and wind is put forward based on the three-stage flight program with passive intermediate section. A discrete process based on pseudo-spectral method is used to solve the problem, which allows converting the initial problem into a nonlinear programming problem with dynamic constraints and aims for the criteria of maximization of the final mass released onto the target orbit.
Application of the proposed solution procedure is illustrated by calculating the optimal control and the corresponding trajectory for two-stage liquid launch vehicle, which places the small spacecraft on the orbit of sun-synchronous at the height of 512 km. The numerical simulation results have demonstrated the effectiveness of the proposed algorithm and allow us to analyze three-stage trajectory parameters with intermediate passive flight phase. It can be noted that in the resulting ascent trajectory, the intermediate passive flight part is a suborbital trajectory with low energy integral, perigee of which is under the surface of the Earth.