On dynamics of relational systems: relativistic case

In the paper the initial stages to obtain the dynamic equation of the relational theory is discussed. As the limiting dynamic equation we use the equations describing the relativistic dynamics of a three-dimensional spatial hypersurface that is composed of a continuum set of arbitrary moving particles and corresponding to the same value of their proper time. The relations describing the internal geometry of the space hypersurface are obtained. The problem of the interpretation of the spatial metrics of the dynamically evolving space hypersurface in the case of a discrete set of particles is discussed.