Stabilized Kepler motion connected with analytic step adaptation

In the publication Baumgarte and Stiefel (1974a) a stabilization of the Keplerian motion was offered by making use of a manipulation of the Hamiltonian. By this stabilization technique the given HamiltonianH(p _i,q _i) is replaced by a new HamiltonianH ^*, which leads to Lyapunov-stable differential equations of motion.Whereas, in the quoted publication, the physical timet was used as the independent variable we now develop a generalization which allows to combine the stabilization with the introduction of a new independent variables. Such a fictitious times is popular for achieving an analytic step-size adaptation (Baumgarte and Stiefel, 1974c). Perturbations of Kepler motion are discussed.