Some ways parameter calculation curvilinear uniformly accelerated motion

TL;DR

The paper addresses the problem of characterizing and transforming to a rigid, curvilinearly uniformly accelerated frame in special relativity. It develops and compares three complementary methods—boosting from an inertial frame, solving inverse kinematics, and solving tetrad motion equations—to obtain consistent motion parameters and an explicit transformation into the accelerated frame. A key result is that the Thomas precession and Wigner rotation cancel for uniformly accelerated motion, so the net rotation is zero; the three methods are shown to be equivalent and yield identical parameter sets. The work provides explicit transformation formulas and demonstrates their compatibility, with potential relevance for future relativistic navigation and astronautics where constant proper acceleration frames may arise.

Abstract

The parameters of uniformly accelerated reference frame s three equivalent ways is calculated. The article also found explicitly transformation to uniformly accelerated reference frame and proved the assertion that Thomas precession and Wigner rotation s in opposite directions and cancel each other out.