Relativistic Dynamics and Electrodynamics in Uniformly Accelerated and in Uniformly Rotating Frames—the Proper Time Expressions

In the current paper we present a generalization of the transforms from the frame co-moving with an accelerated particle, for either rectilinear or circular motion, into an inertial frame of reference. The solution is of great interest for real time applications, because earth-bound laboratories are inertial only in approximation. The motivation is that the real-life applications include accelerating and rotating frames with arbitrary orientation more often than the idealized case of inertial frames; our daily experiments happen in the laboratories attached to the rotating Earth. Our paper is divided into two main sections, the first section deals with dynamics, i.e., forces, the second section deals with electromagnetism, i.e., Lorentz force and electromagnetic potentials, both expressed in terms of proper time.