A Simple Method for the Determination of Angular Velocity and Acceleration of a Spherical Motion Through Quaternions

Given a quaternion representation of a spherical motion of a rigid body with respect to another body, acting as a reference frame, this contribution presents a simple and straightforward method for determining both the angular velocity and angular acceleration of the moving body with respect to the reference frame. Instead of employing orthogonal matrices or their linear invariants, this contribution makes use of quaternions avoiding, in this way, the series of matrix identities or theorems that are required in a pair of previous approaches.