Classical Physics

    

Deriving Rotational Quaternions Using Pivot Vectors

Authors: Russell P. Patera

Pivot Vectors are used to derive the orthonormal triad that forms the basis vectors of rotational quaternions. Pivot Vectors are also used to derive Hamilton’s rules for quaternion algebra, which forms the foundation of quaternion parameterization of attitude. The concepts of simultaneous rotations and sequential rotations are used with Hamilton’s rules to derive the quaternion composition rule for rotations. The quaternion derivation of the rotation composition rule is compared to the Pivot Vector derivation to clarify the respective attitude parameterizations.

Comments: 8 Pages.

Download: PDF

Submission history

[v1] 2026-02-20 20:01:55

Unique-IP document downloads: 71 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus