Relativistic fictitious forces in uniformly rotating frames

In the current paper, we present a generalisation of the transforms from the frame co-moving with an accelerated particle for uniform 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 orientations more often than the idealised case of inertial frames; our daily experiments happen in the laboratories attached to the rotating Earth. Our paper is divided into three main sections, the first section deals with the theory of the dynamics, i.e., forces, the second section deals with the application of the theory to the derivation of the relativistic fictitious forces (Coriolis, centrifugal and Euler) occurring in the rotating frame. The third section deals with the relativistic fictitious forces in the quasi-inertial frame of the lab. We will show that there is not only a fictitious force that emerges in the rotating frame but also a fictitious power. The present paper is of interest to the researchers working with any type of circular particle accelerator. Copyright © 2021 Inderscience Enterprises Ltd.