Читать книгу Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren - Страница 61

Consider the following rotation.

(3.66)

This rotation can be described by the following matrix equations expressed in two different reference frames and .

(3.67)

(3.68)

In the above equations, and are the rotation matrices that represent the same rotation operator in and , respectively. That is,

(3.69)

(3.70)

As for the vectors and , their matrix representations are related to each other as follows by the transformation matrix :

(3.71)

(3.72)

When Eqs. (3.71) and (3.72) are substituted, Eq. (3.68) becomes

(3.73)

When Eqs. (3.67) and (3.73) are compared, it is seen that the matrices and are related to each other as follows by using both and :

(3.74)