Rotation of Vectors and Rotation Matrices

A vector may be acted upon, simultaneously or successively, by two kinds of displacement operators. One of them is a rotation operator and the other is a translation operator. This chapter is devoted to the rotation of vectors and the rotation operators that rotate vectors. The vector equation is obtained as the Rodrigues formula. The matrix equation is written in terms of the rotation matrix, which is the matrix representation of the rotation operator in the selected reference frame. The chapter presents the salient mathematical properties of the rotation matrices that can be used conveniently in the symbolic manipulations concerning rotational kinematics. Demonstrative examples are also included.