Читать книгу Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren - Страница 15

A vector is defined as an entity that can be described by a magnitude and a direction. In this book, it is assumed that all the vectors belong to the three‐dimensional Euclidean space.

The magnitude of a vector is denoted as shown below.

(1.1)

A unit vector such as is defined so that its magnitude is unity. That is,

(1.2)

A vector can be expressed as follows by means of a unit vector , which is introduced to indicate the direction of .

(1.3)

In Eq. (1.3), v is defined as the scalar value of with respect to .

Note that the magnitude of a vector is the absolute value of its scalar value. That is,

(1.4)

Note also that the scalar value v can be positive, negative, or zero, but the magnitude can only be positive or zero.

The sign variability of the scalar value is demonstrated in the following equation.

(1.5)

According to Eq. (1.5), the scalar values of the same vector with respect to and are v and v^′ = − v, respectively.