Reduction of the two-body problem with central interaction on simply connected spaces of constant sectional curvature

Abstract

The problem of two particles with central interaction on simply connected spaces of a constant curvature was considered. Due to the absence of the Galilei transformation in this case the reduction to the dynamic problem in four-dimensional phase space was carried out using the Marsden-Weinstein method. Canonically conjugate coordinates were found. The classification of reduced dynamic systems was given. For some of them conditions of the existence global solutions for dynamic equations with attractive potentials were found. The comparison of the structure of obtained Hamiltonians with integrals of the one-particle problem with Bertrand's potentials was carried out.