18-06U

A pointlike particle mechanics in the de Sitter space-time is considered. In terms of conformally flat parametrization of this space-time it is constructed the realization of a group of its symmetry O(1,4), the point-like particle action, its Lagrangian and Hamiltonian description. Within the formalism of Fokker action integrals the classical mechanics of interacting particles in the de Sitter space-time is constructed. A general form of de Sitter-invariant Fokker action integral is derived. It is shown that the known in the literature examples of scalar and electromagnetic interactions agree with the results obtained here. Equation of motion of a point charge in an external electromagnetic field where the radiation reaction is taken into account is proposed.