Why is it that I can't describe with words the orientation of a 3D object (i.e. I can't give a set of angles that uniquely describe it). On the other hand, I can mimic fairly precisely it's orientation with my hand to describe it. A one dimensional object however, is easy to describe with an angle such as a clock at +90 degrees is 12 o' clock. So, a 1-D object with a 1-D gyro attached, you can integrate and find the relative angle easily (assuming no bias and not worrying about the need for an accelerometer). In the case of a 3-D object you have 3 orthogonal gyros. Then what numbers do you get when you integrate those? Obviously not the 3 angles to describe that 3-D object or it would be too easy and transformations and quaternions wouldn't be needed. The intuition of the above questions could be answered with the following posed design: 1. Hook a 3 axis gyro up to a computer. 2. Create a program that transforms the 3 rates to a quaternion. 3. Turn the quaternion into a rotation matrix to animate the rotational motion of the gyro. What this does is mimics your rotations of the gyro by your hand and animates it on the computer screen. In my opinion this is the simplest possible design to demonstrate the movements of an external 3D object in terms of a quaternion. If one could realize this design in a more precise outline, I could almost completely understand the essentials of how a quaternion works. I've searched hundreds of websites, and the math is everywhere, but the above questions and answers are not. Please fill in the example or let me know of a source that describes this. Thanks.