https://doi.org/10.1140/epjp/s13360-022-03558-x
Regular Article
Non-inertial torques and the Euler equation
Department of Mathematics and Physics, SUNY Polytechnic Institute, 13502, Utica, NY, USA
Received:
3
October
2022
Accepted:
1
December
2022
Published online:
14
December
2022
The key equation describing the rotational dynamics of a rigid body is 
which can be understood based on the Newton’s second and third laws of motion together with the assumption of mutual centrality of the internal forces and is valid in an inertial coordinate system. While this equation is written down by an inertial observer, for practical purposes, it is efficiently worked out within a non-inertial rotating ancillary coordinate system along the principle axes of the rigid body. This results in the famous Euler equation for rotation of the rigid bodies. We show that it is also possible to describe the rotational dynamics of a rigid body from the point of view of a non-inertial observer (rotating with the ancillary coordinate system), provided that the non-inertial torques are taken into account. We explicitly calculate the non-inertial torques and express them in terms of physical characteristics of the rigid body. We show that the resulting dynamical equations exactly recover the Euler equation.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. 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.
