Motivated by the requirement for pinpoint landing in future Mars missions, we consider the problem of minimum-fuel powered terminal descent to a prescribed landing site. The flrst-order necessary conditions are derived for the case of free initial and flnal thrust directions, clarifying the characteristics of the minimum-fuel solution. The most general thrust magnitude proflle has a max-min-max structure. When the initial and flnal thrust directions are specifled, the minimum-fuel solution is changed, relative to the free initial and flnal thrust direction case, only in initial and flnal boundary-layers where there are maximum rate thrust direction adjustments. Minimum-fuel solutions are obtained numerically to illustrate the optimal strategies from several starting conditions.
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Topcu et al. (2005) studied this question.
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