Explicit Newmark/Verlet algorithm for time integration of the rotational dynamics of rigid bodies

We reformulate the traditional velocity based vector-space Newmark algorithm for the rotational dynamics of rigid bodies, that is for the setting of the SO(3) Lie group. We show that the most naive re-write of the vector space algorithm possesses the properties of symplecticity and (almost) momentum conservation. Thus, we obtain an explicit algorithm for rigid body dynamics that matches or exceeds performance of existing algorithms, but which curiously does not seem to have been considered in the open literature so far