Covariant teilor's series and geodetic structure of space-time

Abstract

Relativistic dynamics of test bodies, space-time geometry are considered in the paper aiming at the development of invariant constructive methods of the extented relativistic system description, their application to the dynamics of test bodies and to the description of gravitation fields. As a result the generalized covariant form of the Terilor's theorem for tensor and spin fields has been given. Managements of the relative movement of test bodies have been obtained; the fundamental algebra has been introduced and investigated; decompositions of main values in normal coordinates and Fermi's coordinates have been given. The paper results may find their field of application in dinamics of relativistic systems, relativistic astrometry, theory of observed spaces, comparison of Riemann's spacesAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio