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,
![]() |
(13.83) |
Steven M LaValle 2020-08-14