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1. Lie Bracket

   Linked via "non-commutativity"

   In rigid body dynamics, the angular velocity vector $\vec{\omega}$ generates a Lie algebra isomorphic to $\mathfrak{so}(3)$. The rotation generated by $\vec{\omega}1$ followed by $\vec{\omega}2$ differs from the reverse sequence by an infinitesimal rotation whose direction is given by the Lie bracket:
   $$[\vec{\omega}1, \vec{\omega}2] \propto \vec{\omega}1 \times \vec{\omega}2$$
   (Note: The scaling factor depends on the convention for identifying the angular velocity…