The trajectory of the launcher in vacuum space can be determined by solving an optimal control problem. The formulation of the problem leads to the Primer vector theory, where the optimal thrust direction, the number and duration of coasting arcs are determined by the appropriate initial conditions of the Lagrangian multiplier corresponding to the velocity vector. The numerical methods required to solve the optimal problem, and hence to derive the nominal optimal trajectory, are not applicable to the flight of a space launcher. Simplified and direct guidance algorithms are required, which are suitable for the implementation of real-time guidance algorithms on the on-board computer. In this Chapter, simple criteria for the duration of the coasting arc after the atmospheric flight are given and the final injection into orbit is studied by means of a time-optimal guidance implemented with simplified models of the launcher dynamics. Furthermore, the Q-guidance algorithm is presented: this guidance algorithm was introduced in the Apollo missions and can be implemented in real time by analytical formulae. Some current launchers implement a real-time tangent linear law for the trust guidance to injection into orbit. This guidance is described here. Applications are given in the problem posed and solved at the end of the chapter.
Ascent Trajectories: Exo-Atmospheric Arc
Springer Aerospace Techn.
2024-12-27
52 pages
Article/Chapter (Book)
Electronic Resource
English
Ascent Trajectories: Atmospheric Arc
Springer Verlag | 2024
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