Formulas for Rotation and Angular Velocity Arising from Shake Table Kinematics and Kirchhoff Rod Model Implementation
Publication: Journal of Engineering Mechanics
Volume 147, Issue 1
Abstract
This technical note presents a pair of formulas to rotate a unit vector to another unit vector and compute the corresponding angular velocity. These formulas arose independently in two of our recent applications: (1) modeling actuator kinematics in a two-degree-of freedom (2-DOF) shaker, and (2) implementation of Kirchhoff rod theory in three-dimensional (3D) for modeling intracranial aneurysm coiling and analysis of electrical conductor nonlinear dynamics. The first formula (for rotation) can be found in the literature. The second formula (for angular velocity), while simple and straightforward, is not found in the literature and is the contribution in this note. This latter formula, due to its simplicity, is likely useful in a number of other applications in computational mechanics and mechanism/robot kinematics.
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Data Availability Statement
No data, models, or code were generated or used during the study.
Acknowledgments
The first author was supported by the Department of Civil, Structural and Environmental Engineering, University at Buffalo; the second and third authors were supported by a grant from Bonneville Power Administration.
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Published In
Journal of Engineering Mechanics
Volume 147 • Issue 1 • January 2021
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Apr 26, 2020
Accepted: Aug 14, 2020
Published online: Oct 31, 2020
Published in print: Jan 1, 2021
Discussion open until: Mar 31, 2021
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