Sequences of co-moving Lorentz frames
type: Item
instance of: scholarly article
title: Sequences of co-moving Lorentz frames
zbMATH Open document ID: 0714.34006
DOI: 10.1016/0022-247X(90)90418-F
author: Harry Gelman
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: The paper presents a new analysis of co-moving sequences of Lorentz reference frames tracking accelerated relativistic particles. The group property of the homogeneous Lorentz transformation written in the most general, coordinate-independent form for inertial frames with arbitrary orientation and velocity implies the composition law that is used to formulate the conditions of any co-moving sequence. These lead to a new differential equation of change which defines entire sequences and selects the frames within a given sequence, \(d\bar R/dt=- \bar Rx\omega_ T-\omega'x\bar R/\gamma\), where \(\bar R\) is an arbitrary rotation dydic, \(\gamma\) a parameter. It is governed by two arbitrary angular velocities, the velocity of Thomas precession \(\omega_ T\) and an arbitrary angular velocity \(\omega'\) between adjacent instantaneous frames. A formal integration of selection equation, which is generally unsoluble in closed form, is outlined using time-ordered operator products. This represents a perturbation solution. Coupled differential equations for the effective axis and angle of the rotation component of the Lorentz transformation are derived. Two specific examples are considered.
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 83A05
zbMATH DE Number: 4175392
zbMATH Keywords: co-moving frames
zbMATH Keywords: Thomas precession
zbMATH Keywords: Fermi-Walker sequence
zbMATH Keywords: homogeneous Lorentz transformation
reviewed by: L. M. Berkovich
MaRDI profile type: Publication
cites work: The Lagrangian in classical field theory
cites work: Q4256628
cites work: Q4595136
cites work: Q4530672
cites work: The second orthogonality conditions in the theory of proper and inproper rotations .I. Derivation of the conditions and of their main consequences
cites work: A note on the time dependence of the effective axis and angle of a rotation
cites work: Q5567065
description: scientific article; zbMATH DE number 4175392