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The orbital motion around a central body is an interesting problemthat involves the theory of artificial satellites and the planetary theoriesin the solar system. Nevertheless some difficult situations appear whilestudying this apparently simple problem, depending on each particularcase. The real problem consists of searching the perturbed solution froma basic two-body motion problem. In addition, the perturbed problemmust be solved using a numerical method and its efficiency depends onthe selected coordinate system and the corresponding time. In fact, localand global errors are not necessarily homogeneously distributed over theorbit. In other words, there is a strong relationship between the spatialdistribution of the selected points and the temporal independent variable. This is particularly dramatic in specially difficult cases. This issue leads us to consider different anomalies as temporal variables, searching for both precision and efficiency. Therefore, we are interested in the study of techniques to integrate the orbital motion equationsusing different anomalies as temporal variables which are functions of oneor more parameters. The final aim of this paper is the minimization of the integration errors using an appropriate choice of the parameter depending on the eccentricityvalue in the family of the generalized Sundman anomalies

A Note on the Use of Generalized Sundman Anomalies in the Numerical Integration of the Elliptical Orbital Motion