摘要：The dynamics of the two-body problem with general mass-loss functions that depend on both the independent variable and the radial distance are studied. These functions have been considered by Docobo and coworkers to explain the so-called "periastron" effect. By means of some appropriate changes of variables we reduce the integration of this problem to a perturbed harmonic oscillator that is solved by means of the Krylov–Bogolioubov (KB) averaging method. By using the fact that the KB method provides approximate solutions that are first-order accurate in the small parameter in intervals of length 1/, we may get first-order accurate solutions for all physical time t ≥ 0 and therefore to study the asymptotic behavior of solutions for all t ≥ 0. These results extend previous studies of the authors for the first Gylden–Mestchersky problem.
