Читать книгу Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren - Страница 38

The first basis vector of a reference frame is rotated successively in two different sequences, which are indicated below. It is required to express the resultant vectors in .

(2.88)

(2.89)

In the first sequence, and are obtained as described below.

(2.90)

(2.91)

Noting that , the vector equations corresponding to Eqs. (2.90) and (2.91) can be written as follows:

(2.92)

(2.93)

In the second sequence, and are obtained as described below.

(2.94)

(2.95)

The corresponding vector equations can be written as follows, like those written for and :

(2.96)

(2.97)