Geodesic
On the solutions of the simplified system of nonlinear differential equations in the motion of four particles in a plane
Problemy fiziki, matematiki i tehniki, no. 3 (2014), pp. 80-84.

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A system describing the motion of four bodies under the action of gravity is considered. By elementary algebraic manipulations a simple system consisting of non-linear differential equations, each of which has a second order is selected. For each simplified system there are sets of constants of interparticle interaction, in which the general solution is meromorphic.
Keywords: movement of four bodies, Painlevé property, meromorphic function.
Mots-clés : constant interaction 
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A. T. Sazonova. On the solutions of the simplified system of nonlinear differential equations in the motion of four particles in a plane. Problemy fiziki, matematiki i tehniki, no. 3 (2014), pp. 80-84. http://geodesic.mathdoc.fr/item/PFMT_2014_3_a14/

[1] F. Kalodzhero, Teoreticheskaya i matematicheskaya fizika, v. 133, Razreshimaya zadacha trekh tel i gipotezy Penleve, 2-e izd., Nauka, M., 2002, 149 pp.

[2] A. T. Lozovskaya, “Test Penleve dlya nekotorykh sistem differentsialnykh uravnenii, svyazannykh s zadachei trekh tel”, Nauka-2009, Sb. st. aspirantov i magistrantov GrGU/GrGU im. Ya. Kupaly, ed. A. F. Pronevich, GrGU, Grodno, 2009, 48–52