On Accelerated Coordinate Systems in Classical and Relativistic Mechanics

Abstract

A simplified discussion is given of the problem of introducing linearly accelerated axes by a method applicable alike to classical and relativistic mechanics. The mathematical method is based on the Lie theory of the 4-dimensional conformal group which is presented in such a way that the transformations leading to accelerated axes are exhibited explicitly. The classical theory is shown to be a degenerate case of the relativistic theory, so that the transformations to accelerated axes have a geometrical interpretation in terms of inversive transformations in both theories.