3D Rotations and Quaternions

This lecture covers 3D rotations, transformations of Rodriguez, quaternions, and 3D homogeneous matrices around an arbitrary vector. The instructor explains the concepts of rotation matrices, direction cosines, and the transition from rotation matrices to the axis and angle of rotation. The lecture also delves into the generalized rotation matrix, considering active transformations with respect to the basic referential. Quaternions are introduced as a generalization of complex numbers, providing an elegant solution to the limitations of rotation matrices. The use of quaternions in expressing rotations and the passage between quaternions and matrices of direction cosines are discussed, along with the composition of rotations and 3D homogeneous matrices.