Rigid Body Dynamics - Stability About Principal Axes - Qualitative Analysis of Spinning Objects

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A demonstration of yaw-pitch-roll from the built-in gyroscope of an iPad .
Free rigid body. First, the stability of the motion for a torque-free rigid body, that is a rigid body which can be approximated as having no external moments on it. We try to give an intuitive explanation as to why pure rotation about any axis is not possible. Instead, there are only three directions about which pure rotation is possible, corresponding to the principal axes. The principal axes can be ordered by the corresponding value of the moment of inertia for rotation about that axis. In general, we have I_max, I_int, I_min, corresponding to the maximum, intermediate, and minimum moment of inertia. We discuss the stability of rotations about these axes: rotation about the maximum and minimum principal axes are stable, whereas ....
rotation about the intermediate axis is unstable .
Why can't we always get pure (steady) rotation about an axis for a free rigid body? Mystery of free rigid body dynamics can be understood by considering internal moments..
Qualitative analysis of spinning objects. We discuss the qualitative analysis of a spinning body, where the body is either spinning rapidly or is a system with a connected rapidly spinning rotor. The approach we mention is useful to develop a qualitative understanding of the expected behavior. We apply the analysis to a gyroscope with a rapidly spinning flywheel, which is suspended from a string. .