Analyzing the angular acceleration vector of a moving rigid body

This paper presents a novel and systematic approach for obtaining the angular acceleration vector of a moving rigid body. The novelty of the proposed method lies in the particular form of writing the pose of the moving rigid body, as well as in the procedure to compute its time derivatives. The derivation process goes directly to the very foundations of rotational motion and exploits the phenomenological connection between orientation, angular velocity, angular acceleration, and spatial motion of a rigid body. Hence, as a remarkable result, a symbolic expression for the angular acceleration vector arises naturally without the need to solve the inverse acceleration problem. The novel and general expression of the angular acceleration vector involves relationships between the position, velocity, and acceleration vectors of three non-collinear points of the body, which can be easily understood and physically interpreted without particular knowledge of specialized techniques or advanced mathematical tools. Due to its vector nature, the expression for the angular acceleration vector proposed in this paper is relatively simple, as well as, it is very robust against computational singularities. Two fully detailed case studies demonstrate the robustness of the proposed angular acceleration vector compared with other expressions appearing in the literature.