Geodesic
Rigorous definition of the reference frame
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2014), pp. 25-36

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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 
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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/