Optimal trajectories for hypersonic launch vehicles

In this paper, we derive a near-optimal guidance law for the ascent trajectory from Earth surface to Earth orbit of a hypersonic, dual-mode propulsion, lifting vehicle. Of interest are both the optimal flight path and the optimal operation of the propulsion system. The guidance law is developed from the energy-state approximation of the equations of motion. The performance objective is a weighted sum of fuel mass and volume, with the weighting factor selected to give minimum gross take-off weight for a specific payload mass and volume.