The exact eigenfunctions for the slewing link of a robot are found, taking into account a rotating inertia at the base and a payload at the tip. These derive from two equivalent formulations (pseudoclamped and pseudopinned) of the boundary value problem relative to the flexible slewing beam. The exactness of the solution makes it possible to prove the equivalence of these two approaches, which differ in the choice of the noninertial rotating frame. The two related dynamic linear models are then found, and a change of coordinates is given. Experimental measurements validate the theoretical results.>