Download Visualizing Quaternions (The Morgan Kaufmann Series in by Andrew J. Hanson PDF

By Andrew J. Hanson

I observed each element within the 3 sphere, in 4D. In a colour i have by no means visible before...

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Using a minimal arc-length quaternion path from the starting to the ending orientation, as introduced in Chapter 10, eliminates the problem. 5 THE URBAN LEGEND OF THE UPSIDE-DOWN F16 Stories about the development of the high-performance F16 military fighter aircraft provide yet another example of a situation in which a proper understanding of 3D orientation issues is absolutely necessary. Although it is not clear whether quaternion technology could have avoided the reported situation, it is perfectly clear that a lucid understanding of the nature of orientation computations, facilitated by the study of quaternion orientations, would not have hurt!

Htm, W. ) 26 CHAPTER 02. 10 When a force F is applied in an attempt to reorient a single gyroscope with angular momentum L to any axis not aligned with the current gyroscope axis, the resulting torque T will change the gyroscope’s direction by as much as 180 degrees. With multiple gyroscopes, the system cannot follow the motion without massive stress on the mechanical system. 8), must therefore be avoided at all costs! We will see in Chapter 14 how to visualize what is happening in gimbal lock, and why it is so difficult to completely avoid it.

3 THE APOLLO 10 GIMBAL-LOCK INCIDENT 23 What is gimbal lock, and why did it become so visible in the Apollo missions? 5, is a mechanical system with three apparent degrees of freedom. 8 shows a schematic diagram of the IMU system. 9, which are taken from a tutorial on gimbal lock compiled into the NASA Apollo 15 transcript [176]. The critical feature is a mechanical gyroscope system, which is designed to maintain constant orientation with respect to the outside world. The gyroscope system is attached to the spacecraft frame using three rotating rings of decreasing diameter.

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