The dynamics of particle motion is investigated within the frame of a relativistic model, constituting an Euclidean space with three real spatial axes and one axis corresponding to the local (eigen) time. An assumption is set forth about the isotropy of this tetrameric space at small velocities of the objects as a consequence of the equivalence principle of the spatial and eigen time coordinates. The equations for trajectories are found, which are classified as the inertial motion. In the three-dimensional spa-tial basis, besides the trivial solutions, they include the accelerated motion in the harmonic and gravitational fields. In the latter case, such a motion can be implemented under the assumption of the two-dimensional nature (or complexity) of the eigen time of the particles. The Laplace invariant is constituted by the real components of the coordinates and velocities.