In this work, various formulations describing the excitation of Earth rotation, originating with the effective angular momentum functions of Barnes et al. <1983>, are assessed in the context of zero or complete coupling between the core and the mantle. Popular formulations have assumed zero coupling for the length of day component but are ambiguous for polar motion. Versions are developed here for the case of arbitrary core-mantle coupling, and employed to derive consistent formulations for both extremes of coupling. Even for complete decoupling, all of the formulations can differ from each other noticeably, depending on the treatment of the oceans and the parameter values employed. It is recommended that agencies responsible for archiving atmospheric and other excitation data consider distributing bare bones, parameter-free time series. A possible inconsistency in all formulations to date is the role of the degree 2 solid earth Love number. If the Chandler wobble takes place with a (near) absence of core-mantle coupling, then prior estimates of the Love number have in reality been measuring its mantle-only component. By implication the mantle may be much more anelastic at a 14-month period than had previously been recognized.