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arXiv · 2212.11789

Euler's Equation via Lagrangian Dynamics with Generalized Coordinates

Dennis S. Bernstein·Ankit Goel·Omran Kouba
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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.

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Dennis S. Bernstein, Ankit Goel, Omran Kouba. 2022-12-22. Euler's Equation via Lagrangian Dynamics with Generalized Coordinates. https://doi.org/10.3390/math11122727

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