Euler's Equation via Lagrangian Dynamics with Generalized Coordinates
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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.