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}
}