MATHEMATICS

On the solutions of the simplified system of nonlinear differential equations in the motion of four particles in a plane

A. T. Sazonova

Y. Kupala Grodno State University, Grodno, Belarus

Abstract: 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, constant interaction, Painlevé property, meromorphic function.

UDC: 517.925

Received: 28.05.2014