https://doi.org/10.1140/epjp/s13360-025-07273-1
Regular Article
Transformation equation for frames undergoing non-uniform acceleration such as SHM and rotational motion
Department of Physics, Assam University, 788011, Silchar, Assam, India
a
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Received:
14
October
2025
Accepted:
30
December
2025
Published online:
20
January
2026
Abstract
Lorentz transformation equations provide us a set of relations between the spacetime coordinates as observed from two different inertial frames. In case, one of the frames is moving with a uniform rectilinear acceleration; we have Rindler’s transformation equations under such a situation. In the present work, we extend the Rindler’s equations to a situation where we have in general non-uniform acceleration. After that we consider the non-inertial frame to undergo simple harmonic motion (SHM), and as a second case, we consider the non-inertial frame to move uniformly along a circle. This set of transformation equations will have applications in various branches of Physics and in general in Astrophysics.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
