Geodesic
Rigorous definition of the reference frame
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2014), pp. 25-36 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A formal definition of the reference frame is given. This definition allows to consider reference frames in most common case without restriction to inertial, uniformly accelerated or rotating frames. Proposed definition is valid for non-relativistic and relativistic cases. A conception of the system of coordinates associated with a reference frame is introduced. It is shown that one of these coordinates can be regarded as temporal coordinate, and the others as spatial ones. It is demonstrated that in the relativistic case non-diagonal spatial-temporal components of the metric tensor are always equal to zero. Inertial, accelerated, and rotating reference frames are considered as examples. Bibliogr. 12.
Keywords: spacetime, congruence of observers, reference frame, temporal and spatial coordinates, metric tensor.
Mots-clés : configuration space 
@article{VSPUI_2014_4_a2,
     author = {O. I. Drivotin},
     title = {Rigorous definition of the reference frame},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {25--36},
     year = {2014},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2014_4_a2/}
}
TY  - JOUR
AU  - O. I. Drivotin
TI  - Rigorous definition of the reference frame
JO  - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
PY  - 2014
SP  - 25
EP  - 36
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VSPUI_2014_4_a2/
LA  - en
ID  - VSPUI_2014_4_a2
ER  - 
%0 Journal Article
%A O. I. Drivotin
%T Rigorous definition of the reference frame
%J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
%D 2014
%P 25-36
%N 4
%U http://geodesic.mathdoc.fr/item/VSPUI_2014_4_a2/
%G en
%F VSPUI_2014_4_a2
O. I. Drivotin. Rigorous definition of the reference frame. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2014), pp. 25-36. http://geodesic.mathdoc.fr/item/VSPUI_2014_4_a2/

[1] Sachs R. K., Wu H., General Relativity for mathematicians, Springer, New York, 1977, 291 pp. | MR | Zbl

[2] Vladimirov Yu. S., Reference frames in gravitation theory, Energoizdat, M., 1982, 256 pp.

[3] The Principle of Relativity, Dover, New York, 1952, 109 pp. | DOI | Zbl | Zbl

[4] Wang C.-C., Mathematical Principles of Mechanics and Electromagnetism, v. B, Electromagnetism and Gravitation, Plenum, New York, 1979, 386 pp.

[5] Landau L. D., Lifshitz E. M., The Classical Theory of Fields, 4th ed., Pergamon, Oxford, 1975, 402 pp. | MR

[6] Collected Papers of Albert Einstein, v. 2, Princeton University, Princeton, 1987, 72–127 | MR

[7] Schmutzer E. (ed.), Exact Solutions of Einstein's Field Equations, Cambridge University, Cambridge, New York, 1980, 426 pp. | MR

[8] Arnowitt R., Deser S., Misner C. W., “The Dynamics of General Relativity”, Gravitation: An Introduction to Current Research, ed. L. Witten, Wiley, New York, 1962, 227–264 | MR

[9] Dirac P. A. M., “Fixation of Coordinates in the Hamiltonian Theory of Gravitation”, Phys. Rev., 114 (1958), 924–930 | DOI | MR

[10] Gourgoulhon E., 3+1 Formalism in General Relativity, Springer, Berlin, 2012, 294 pp. | MR | Zbl

[11] Weinberg S., Gravitation and Cosmology, Wiley, New York, 1972, 657 pp.

[12] Fock V. A., The Theory of Space, Time and Gravitation, MacMillan, New York, 1964, 411 pp. | MR