Angular Velocity vs. Orientation Angles
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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: . 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:

avel_f01.gif (3342 bytes)    Figure 1

   [1]

or

   [2]

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

   [3]

 

Young-Hoo Kwon, 1998-