On Singularity of Rigid-Body Dynamics Using Quaternion-Based Models

It is well known that use of quaternions in dynamic modeling of rigid bodies can avoid the singularity due to Euler rotations. This paper shows that the dynamic response of a rigid body modeled by quaternions may become unbounded when a torque is applied to the body. A theorem is derived, relating the singularity to the axes of the rotation and applied torque, and to the degrees of freedom of the body in rotation. To avoid such singularity, a method of equivalent couples is proposed.