Deriving Euler’s Equation for Rigid-Body Rotation via Lagrangian Dynamics with Generalized Coordinates

Dennis S. Bernstein, Ankit Goel and Omran Kouba ()
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Dennis S. Bernstein: Aerospace Engineering Department, University of Michigan, Ann Arbor, MI 48109, USA
Ankit Goel: Mechanical Engineering Department, University of Maryland, Baltimore County, MD 20742, USA
Omran Kouba: Department of Mathematics, Higher Institute for Applied Sciences and Technology, Damascus 31983, Syria

Mathematics, 2023, vol. 11, issue 12, 1-8

Abstract: Euler’s equation relates the change in angular momentum of a rigid body to the applied torque. This paper uses 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, quaternions. This paper fills a gap in the literature by using generalized coordinates to parameterize the angular velocity vector and thereby transform the dynamics obtained from Lagrangian dynamics into Euler’s equation for rigid-body rotation.

Keywords: angular velocity; rotation; quaternions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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