Название | Kinematics of General Spatial Mechanical Systems |
---|---|
Автор произведения | M. Kemal Ozgoren |
Жанр | Математика |
Серия | |
Издательство | Математика |
Год выпуска | 0 |
isbn | 9781119195764 |
(1.14)
1.3.2 Cross Product
The cross product (a.k.a. vector product) of two vectors
(1.15)
In Eq. (1.15), as defined before, θpq is the angle measured from
If
The sense of
Since, by definition,
(1.16)
(1.17)
If sin θpq = 0, i.e. if
(1.18)
If the order of
(1.19)
According to Eq. (1.12), θqp = θpq. However, according to the right‐hand rule,
(1.20)
Therefore,
(1.21)
1.4 Reference Frames
In the three‐dimensional Euclidean space, a reference frame is defined as an entity that consists of an origin and three distinct noncoplanar axes emanating from the origin. The origin is a specified point and the axes have specified orientations. More specifically, the axes of a reference frame are called its coordinate axes. For the sake of verbal brevity, a reference frame may sometimes be called simply a frame. A reference frame, such as the one shown in Figure 1.1, may be denoted in one of the following ways, which convey different amounts of information about its specific features.
(1.22)
Figure 1.1 A reference frame.
In Eq. (1.22), A is the origin of