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.
Addenda to “On Singularity of Rigid-Body Dynamics Using Quaternion-Based Models”
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.
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Choi, H., and Yang, B. (May 23, 2013). "Addenda to “On Singularity of Rigid-Body Dynamics Using Quaternion-Based Models”." ASME. J. Appl. Mech. July 2013; 80(4): 041029. https://doi.org/10.1115/1.4023108
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