[en] The Schroedinger equation for a three-particle system in the total-angular-momentum J representation is reduced to a system of J+1 three-dimensional equations in prolate spheroidal coordinates. For the corresponding three-dimensional nonseparate spectral problem the Rayleigh-Ritz variational functional is constructed and boundary conditions are found for the wave functions of discrete spectrum. Final formulation of the problem is adapted for applying variational and variational-difference methods for numeri-- cal solving of the three-body problem