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Research Papers

Addenda to “On Singularity of Rigid-Body Dynamics Using Quaternion-Based Models”

[+] Author and Article Information
Homin Choi

Graduate Student

Bingen Yang

Professor
Fellow ASME
e-mail: bingen@usc.edu
Department of Aerospace and Mechanical Engineering,
University of Southern California,
3650 McClintock Avenue, Room 430,
Los Angeles, CA 90089-1453

1Corresponding author.

Manuscript received June 28, 2012; final manuscript received November 21, 2012; accepted manuscript posted November 21, 2012; published online May 23, 2013. Assoc. Editor: Alexander F. Vakakis.

J. Appl. Mech 80(4), 041029 (May 23, 2013) (3 pages) Paper No: JAM-12-1277; doi: 10.1115/1.4023108 History: Received June 28, 2012; Accepted November 21, 2012; Revised November 21, 2012

Although quaternions are singularity-free in modeling and analysis of rigid bodies in three-dimensional motion, description of torques may lead to unbounded response of a quaternion-based model. This paper gives theorems on the conditions of torque-induced singularity in four coordinate systems: inertial frame, body frame, Euler basis, and dual Euler basis. According to the theorems, torques applied in an inertial frame or a body frame or a Euler basis will never cause unbounded motion; torques applied in a dual Euler basis, however, may lead to unbounded motion.

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Grahic Jump Location
Fig. 1

A sequence of Euler rotations: (a) yawing ψ; (b) pitching ϕ; (c) rolling θ

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