The aim of this article is to make some geometric remarks andsome preliminary calculations in order to construct the optimalatmospheric arc of a spatial shuttle (problem of reentry on Earthor Mars Sample Returnproject). The system describing the trajectories is indimension 6, the control is the bank angle and the cost is thetotal thermal flux. Moreover there are state constraints (thermalflux, normal acceleration and dynamic pressure). Our study ismainly geometric and is founded on the evaluation of theaccessibility set taking into account the state constraints. Wemake an analysis of the extremals of the Minimum Principle in thenon-constrained case, and give a version of the Minimum Principleadapted to deal with the state constraints.
