ANALYTICAL PROPERTIES OF SOLUTIONS OF THE PROBLEM OF THE MOTION OF FOUR BODIES IN THE PLANE
Abstract
The purpose of the study is to establish the analytical properties of solutions of nonlinear differential equations describing the planar motion of four bodies. 50 sets of constant values of interparticle interactions in the problem of four bodies in the plane are found, at which the components of the general solution are the meromorphic functions, as well as 15 sets, at which the corresponding systems have no Painlevé property. The results obtained can be applied in the analytic theory of differential equations, as well as for solving the problems of cosmic dynamics.
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