Conclusion

This paper presented the flat-earth resolution of four space trajectory problems: constant acceleration ballistic firing, constant acceleration in-orbit injection, variable thrust vertical firing, variable thrust in-orbit injection.

These problems have been chosen for their academic interest, but also for their practical value in the pre-project phase. In each case, analysis of the optimal control problem leads to a reduced-dimension system (one or two unknowns) that is easy to solve. The solutions obtained give an order of magnitude, which must then be refined using more complex simulation methods. The main theoretical results derived from these flat-earth solutions are summarized below.