An improved algorithm to develop semi-analytical planetary theories using Sundman generalized variables

摘要

One of the main problems in celestial mechanics is the construction of analytical theories of planetary motion. The most common solution of this problem is arranged by means of Poisson series developments. These developments depend on the selection of the anomaly to be used as temporal variable. In this paper we develop an improved algorithm in order to use arbitrary anomalies included in the family of the generalized Sundman anomalies as temporal variables.