Скачать книгу

      Suppose a vector images is rotated into another vector images. This operation is expressed by the following equation as observed in a reference frame images.

      (2.46)equation

      Since a rotation operator does not change the magnitude of the vector it rotates, the following equations can be written.

equation equation

      Owing to its orthonormality, the inverse of images can be obtained by using Eq. (2.14), which is repeated below for the sake of convenience.

      The matrix images can be expressed as follows in terms of its columns:

      (2.54)equation

      Since the kth basic column matrix images picks up the kth column of the matrix it multiplies, images can be obtained as follows together with the interpretation that images.

      Since images is assumed to be a right‐handed reference frame, its basis vectors satisfy the following set of cross product equations.