Generalized Gylden-Type Systems in Universal DS-Like TR-Variables

Scheifele (1970) applied Delaunay-Similar (DS) elliptic Keplerian elements (with the true anomaly as the independent variable) to the J2 Problem in Artificial Satellite Theory, making an element of the true anomaly. Deprit (1981) views Scheifele’s TR-mapping as an extension of Hill’s transformation from a 6-dimensional phase space to an enlarged, 8-dimensional one. To adapt this approach to elliptic-type two-body problems with a time-varying Keplerian parameter μ(t), Floía (1997, §3, §4) treated a Gylden system (Deprit 1983) and derived “Delaunay-Similar” variables via a TR-like transformation. Now we extend our treatment to perturbed Gylden systems, and modify the TR-map to deal with any kind of two-body orbit. We work out our generalization and the resulting variables within a unified pattern whatever the type of motion, in terms of universal functions (Stiefel & Scheifele 1971, §11; Battin 1987, §4.5, §4.6) and auxiliary angle-like parameters.