title: On the rotational equations of motion in rigid body dynamics when using Euler parameters.
abstract: Many models of three-dimensional rigid body dynamics employ Euler parameters as rotational coordinates. Since the four Euler parameters are not independent, one has to consider the quaternion constraint in the equations of motion. This is usually done by the Lagrange multiplier technique. In the present paper, various forms of the rotational equations of motion will be derived, and it will be shown that they can be transformed into each other. Special attention is hereby given to the value of the Lagrange multiplier and the complexity of terms representing the inertia forces. Particular attention is also paid to the rotational generalized external force vector, which is not unique when using Euler parameters as rotational coordinates.
authors.affiliation: Johannes Kepler University of Linz, Altenbergerstr. 69, 4040 Linz, Austria.
authors.forename: Karim
authors.initials: K
authors.lastname: Sherif
authors.affiliation: Faculty of Engineering and Environmental Sciences, University of Applied Sciences Upper Austria, Stelzhamerstr. 23, 4600 Wels, Austria.
authors.forename: Karin
authors.initials: K
authors.lastname: Nachbagauer
authors.affiliation: Faculty of Engineering and Environmental Sciences, University of Applied Sciences Upper Austria, Stelzhamerstr. 23, 4600 Wels, Austria.
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Steiner
keywords: Euler parameter; Generalized force vector; Gyroscopic moment; Rotational equations of motion