Gylden-Mescerskii problem

Mathematics

Scientific paper

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Binary Stars, Stellar Evolution, Stellar Mass Ejection, Two Body Problem, Differential Equations, Symmetry, Transformations (Mathematics), Variational Principles

Scientific paper

The classical non-stationary two-body Gylden-Mescerskii (Gylden 1889, Mescerskii 1893) problem for describing double-star evolution with secular mass loss due to photon and corpuscular activity is investigated using differential equation transformation methods. The possible mass variation laws for reducing the equation to an autonomous form by transformation are given. Symmetry properties are also investigated and integrable cases from the group point of view are reviewed. Finite transformation groups permitting the division of the problem of intergrating the equation into noncrossing classes in accordance with mass variation laws are constructed. Finally, it is intended that the use of the mass variation laws should allow a physically realizable picture of the motion.

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