Poincaré-Similar Variables Including J ₂-Secular Effects

Abstract

In a previous paper we had defined a set of eight generalized canonical Delaunay- Similar (CDS) variables incorporating the first-order secular effects present in the Main Problem in the Theory of Earth’s Artificial Satellite. The new CDS set wsls derived by means of a canonical transformation whose generating function is inspired by Deprit’s radial intermediary and can be considered as a generalization of a canonical set introduced by Scheifele. When applied to Deprit’s intermediary, the proposed variables lead to a simple solution, the momenta being constant and the co-ordinates being either a constant or a linear function of the independent variable. As a further step, a set of generalized Poincaré-Similar (PS) canonical variables corresponding to the aforesaid DS ones is now constructed; the new GPS set also exhibits the same feature of containing the whole first-order secular contribution of the J₂ zonal harmonic of the Earth’s potential and is free from singularities.