GENERALIZATION OF COORDINATE TRANSFORMATIONS BETWEEN ACCELERATED AND INERTIAL FRAMES – GENERAL FORMULAS OF THOMAS PRECESSION
A. SFARTI *
387 Soda Hall, University of California, Berkeley, USA.
*Author to whom correspondence should be addressed.
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. Though prior solutions exist, they are restricted to the particular cases of directions of motion aligned with the coordinate axes. It is our intent to produce a blueprint for generalizing the solutions to the arbitrary directions of motion. 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. We conclude by deriving the general form of Thomas precession as an immediate application of arbitrary orientation of the axis of rotation with respect to the measuring frame.
Keywords: Accelerated motion, general coordinate transformations, accelerated particles, Thomas precession