Euler's Equation via Lagrangian Dynamics with Generalized Coordinates

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2212.11789.pdf (642.09 KB)

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https://arxiv.org/abs/2212.11789

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https://doi.org/10.48550/arXiv.2212.11789
 http://hdl.handle.net/11603/26635

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UMBC Mechanical Engineering Department
UMBC Faculty Collection

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https://orcid.org/0000-0002-4146-6275

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2022-12-22

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journal articles
preprints
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Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)

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Abstract

Euler’s equation relates the change in angular momentum of a rigid body to the applied torque. This paper fills a gap in the literature by using Lagrangian dynamics to derive Euler’s equation in terms of generalized coordinates. This is done by parameterizing the angular velocity vector in terms of 3-2-1 and 3-1-3 Euler angles as well as Euler parameters, that is, unit quaternions.