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The angular orientation angles can also be used in
the computation of the angular velocity of the object. By taking the time-derivatives of
the orientation angles, one can obtain three independent angular velocities:
or
where, wB/A = the angular velocity of frame B relative to frame A, and f, q, and y = the three orientation angles of frame B relative to frame A. [10] shows the angular velocity of frame B relative to A described in frame B while [11] shows the same vector described in frame A. Choose the right form of angular velocity depending on your needs. If the global angular velocity of frame A (wA) is available, the actual angular velocity of frame B is
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© Young-Hoo Kwon, 1998- |
. One thing important
here is the directions of the three angular velocity vectors. The direction of the
first rotation (
) is about the X / X'
axis shown in Figure 1 while the second rotation (
) is about the Y' / Y" axis. The third
rotation (
) is about the Z" / Z'"
axis. For vector addition, it is necessary to transform the angular velocity vectors
to a common reference frame:
Figure 1
[1]
[3]