Summary: The representation of rotations and of the corresponding angular velocity commonly used in rigid body dynamics are revisited using an abstract tensorial approach. In order to do so, Rodrigues’ formula is recalled and the related angular velocity vector is derived. This paper focuses on the analysis of successive rotations and especially a proof of the addition theorem for the angular velocity of successive rotations is presented in a rational manner. Following the discussion of successive rotations and the proof of the addition theorem, the treatment of successive rotation in the current literature on rigid body mechanics is discussed in a review.
For the entire collection see [Zbl 1471.74003].