On a special transformation to a non-inertial, radially rigid reference frame

We discuss the conditions under which a body, moving non-inertially in Minkowski space, can preserve its size. Under these conditions, using a series expansion of the generalized Lorentz transformation, we find a coordinate transformation connecting the laboratory inertial reference frame S and the rigid non-inertial reference frame s which moves without its own rotation with respect to S. Direct consequences of this transformation are: (a) desynchronization, in system s, of the coordinate clocks of s which were previously synchronized in S, and (b) a kinematic contraction of a ruler of system s observed in S. We also consider the dependence of the transformation vector parameter on the proper coordinates of s.