Gyldén model: The slowly changing equivalent gravitational parameter (Q1373716)

In the two-body problem, the authors assume the following law for the variation of the equivalent gravitational parameter: \(\mu(t)= \mu_0+ \varepsilon \overline\mu (\varepsilon\tau)\), \(\varepsilon\ll \mu_0\). For the case of \(\overline\mu\) being \(O(1)\), they obtain a solution via Lissajous variables and Lie-Hori normalisation. For the case of both \(\overline\mu\) and \({d\mu\over dk}\) being \(O(1)\), Delaunay variables and von Zeipel method are used for the approximate solution. Conclusions are drawn on the size of the osculating ellipse, and on the stability of the pericenter and longitudes.