- Hamilton.
- mathematically it's sort sort of an expanded complex number. Not just an extra i, but i, j, and k.
- unfortunate element order
in Wertz's book on "Spacecraft Attitude Control".
Therefore also in one of Matlab's toolboxes.
- unfortunately, order and interpretation varies too.
- one day, put memo PL-18-052 here.
- also called "versor".
- for attitudes, use normalized quaternion.
- that means one element is redundant.
I first met quaternions in my work on the ISO satellite. Later I found them extremely useful in mechanisms, and then again in haptic rendering.
- they can be "almost" intuitive ( examples ).
First in 3D haptic rendering, and later again in tracking the kinematics of the Simodont dental trainer mechanism, and my exoskeletons.
- Euler angles.
- Amy de Butleir.
- order matters.
- exoskeletons, ADL gimbal.
- forward and inverse kinematics.
- add end point positions too.
- small relative rotations in the "control error",
needed because of the extreme difference
between the pointing accuracy
and the full 180° slewing range.
- infinitesimal rotations in "attitude propagation", in simulation.
- rigid body rotations in VR (haptic rendering).
- ( 1, 0, 0, 0 )