  The long-term dynamics of perturbed Keplerian motion is usually analyzed in
simplified models as part of the preliminary design of artificial satellites
missions. It is commonly approached by averaging procedures that deal with
literal expressions in expanded form. However, there are cases in which the
correct description of the dynamics may require full, contrary to simplified,
potential models, as is, for instance, the case of low-altitude,
high-inclination lunar orbits. In these cases, dealing with literal expressions
is yet possible with the help of modern symbolic algebra systems, for which
memory handling is no longer an issue. Still, the efficient evaluation of the
averaged expressions related to a high fidelity potential is often jeopardized
for the expanded character of the output of the automatic algebraic process,
which unavoidably provides huge expressions that commonly comprise tens of
thousands of literal terms. Rearrangement of the output to generate an
efficient numerical code may solve the problem, but automatization of this kind
of post-processing is a non trivial task due to the ad-hoc heuristic
simplification procedures involved in the optimization process. However, in
those cases in which the coupling of different perturbations is not of
relevance for the analysis, the averaging procedure may preserve the main
features of the structure of the potential model, thus avoiding the need of the
typical blind computer-based brut force perturbation approach. Indeed, we show
how standard recursions in the literature may be used to efficiently replace
the brut force approach, in this way avoiding the need of further
simplification to improve performance evaluation. In particular, Kaula's
seminal recursion formulas for the gravity potential reveal clearly superior to
the use of both expanded expressions and other recursions more recently
proposed in the literature.
