Addenda to “On Singularity of Rigid Body Dynamics Using Quaternion Based Modelsâ€‌

Abstract

Although quaternions are singularityfree in modeling and analysis of rigid bodies in threedimensional motion, description of torques may lead to unbounded response of a quaternionbased model. This paper gives theorems on the conditions of torqueinduced 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.