M. Nouri-Zonoz, H. Ramazani-Aval, R. Gharachahi
Unlike the Lorentz transformation which replaces the Galilean transformation among inertial frames at high uniform velocities, there seems to be no such a consensus in the case of rotating frames and the common practice is the use of the classical Galilean rotational transformation. There has been some attempts to generalize this transformation to high rotational velocities (i.e high angular velocities or large radial distances). Here we introduce a modified version of one of these transformations proposed by Philip Franklin in 1922, which is shown to resolve some of its shortcomings specially with respect to the corresponding spacetime metric in the rotating frame. The modified transformation is reinterpreted in terms of non-inertial observers sitting at non-zero radii and the corrersponding metric in rotating frame is shown to be consistent with the one obtained through Galilean rotational transformation for points close to the axis. Spatial distances and time intervals based on the same spacetime metric are also discussed.
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http://arxiv.org/abs/1208.1913
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