Читать книгу Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren - Страница 40

Equation (2.76) is verified here as a follow‐up to Example 2.2.

Starting with Eq. (2.75), the powers of can be expressed as follows:

Thus, for all k ≥ 0, it happens that

(2.106)

On the other hand, the following Taylor series expansion can be written for .

(2.107)

Using Eq. (2.106) and noting that , Eq. (2.107) can be written in the following factorized form.

(2.108)

Hence, as the verification of Eq. (2.76), Eq. (2.108) implies that

(2.109)