arXiv:2212.11789 Abstract | arXiv Analytics

arXiv:2212.11789 [math.DS]Abstract References Reviews Resources

Euler's Equation via Lagrangian Dynamics with Generalized Coordinates

Dennis S. Bernstein, Ankit Goel, Omran Kouba

Published 2022-12-22Version 1

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.

Categories: math.DS

Keywords: lagrangian dynamics, generalized coordinates, eulers equation relates, angular velocity vector, euler parameters

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