Before revision:  Properties of the presented algorithms share recursive structure in common with classical methods such as the Composite-Rigid-Body Algorithm . The algorithms presented are of the lowest possible order: O(Nd) for the Coriolis Matrix and O(Nd^2) for the Christoffel symbols, where N is the number of bodies and d is the depth of the kinematic tree.
After revision:  Properties of the presented algorithms share recursive structure in common with classical methods such as the Composite-Rigid-Body Algorithm and are of the lowest possible order: O(Nd) for the Coriolis Matrix and O(Nd^2) for the Christoffel symbols, where N is the number of bodies and d is the depth of the kinematic tree.