To express the change in the moment of momentum in detail, the concept of a differential rotation is needed. In the plane, it is straightforward to define ; however, for , it is more complicated. One choice is to define derivatives with respect to yaw-pitch-roll variables, but this leads to distortions and singularities, which are problematic for the Newton-Euler formulation. Instead, a differential rotation is defined as shown in Figure 13.11. Let denote a unit vector in , and let denote a rotation that is analogous to the 2D case. Let denote the angular velocity vector,
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Steven M LaValle 2020-08-14