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Gylden-Meščerskii problem

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Abstract

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.

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Authors and Affiliations

  1. Kuybyshev State University Kuybyshev, USSR

    L. M. Berković

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  1. L. M. Berković
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To Professor G.N. Duboshin on his 75th Birthday.

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Berković, L.M. Gylden-Meščerskii problem. Celestial Mechanics 24, 407–429 (1981). https://doi.org/10.1007/BF01230399

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