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 ϵ in intervals of length 1/ϵ, 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.

研究了具有依赖于自变量和径向距离的一般质量损失函数的二体问题的动力学。Docobo 和同事认为这些函数可以解释所谓的“periastron”效应。通过一些适当的变量变化，我们将这个问题的积分减少到一个扰动谐振子，该谐振子是通过 Krylov-Bogolioubov (KB) 平均方法解决的。利用 KB 方法在长度为 1/ ϵ 的区间内在小参数ϵ内提供一阶准确的近似解这一事实，我们可以得到所有物理时间t ≥ 0 的一阶准确解，因此研究所有t解的渐近行为 ≥ 0。这些结果扩展了作者之前对第一个 Gylden-Mestchersky 问题的研究。