The main problem in satellite theory revisited

Using the elimination of the parallax followed by the Delaunay normalizatio n, we present a procedure for calculating a normal form of the main problem (J(2) perturbation only) in satellite theory. This procedure is outlined i n such a way that an object-oriented automatic symbolic manipulator based o n a hierarchy of algebras can perform this computation. The Hamiltonian aft er the Delaunay normalization is presented to order six explicitly in close d form, that is, in which there is no expansion in the eccentricity. The co rresponding generating function and transformation of coordinates, too leng thy to present here to the same order; the generator is given through order four.