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The analog of velocity? for rotational movement.
For rotation in a plane inside a Cartesian space $\mathbb{R}^n$ the angular velocity is a bivector in $\wedge^2 \mathbb{R}^n$ of the form
where $e_1$ and $e_2$ are unit vector spanning the plane of rotation, and where $\dot \omega$ is the magnitude of the angular velocity.
Of $n = 3$ (and only then) can we identify bivectors with plain vectors (by the dual operation induced by the Hodge star operator). Often in the literature only this “angular velocity vector” in 3 dimensions is considered.
Standard discussion of angular velocity in $d \leq 3$ is for instance in
The more general discussion in terms of bivectors is found for instance in Geometric Algebra-style documents, such as
Chris Doran, Anthony Lasenby, Geometric Algebra for Physicists Cambridge University Press
Physical applications of geometric algebra (pdf)