Celestial mechanics

, Volume 24, Issue 4, pp 407-429

First online:

Gylden-Meščerskii problem

  • L. M. BerkovićAffiliated withKuybyshev State University Kuybyshev

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Classical non-stationary two-body problem, described by the equation of the form
$$\ddot r = - \mu (t)\frac{r}{{r^3 }}$$
is investigated using differential equation transformation methods developed by the author.

All laws of mass variation for which Gylden-Meščerskii problem is reduced to autonomous form are stated. The problem symmetry properties are investigated and reviews of integrable cases from the group point of view are made.