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Euler's Equation via Lagrangian Dynamics with Generalized Coordinates

Dynamical Systems 2023-08-21 v1

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.

Keywords

Cite

@article{arxiv.2212.11789,
  title  = {Euler's Equation via Lagrangian Dynamics with Generalized Coordinates},
  author = {Dennis S. Bernstein and Ankit Goel and Omran Kouba},
  journal= {arXiv preprint arXiv:2212.11789},
  year   = {2023}
}
R2 v1 2026-06-28T07:49:01.975Z