Читать книгу Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren - Страница 28

This chapter is devoted to the rotation of vectors and the rotation operators that rotate vectors. The rotation of a vector is expressed both as a vector equation and as a matrix equation written in a selected reference frame. 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 expression of the rotation matrix is obtained in terms of the angle of rotation and the unit vector along the axis of rotation. It is shown that the rotation matrix can be expressed very compactly in the exponential form. This chapter also 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.