Summary: A procedure is outlined for a conservative system which makes it possible to go from a Lagrangian of a librating system to the corresponding equations of motion in the Eulerian form. The transition does not require a choice of rotational coordinates and makes use of angular velocities and direction cosines directly. The procedure thus synthesizes attractive features of two classical approaches and has far reaching consequences: it is particularly useful in formulating equations of motion for complex flexible systems of contemporary interest. For the case of a satellite with two flexible plate-type appendages, for example, the approach reduced the formulation time to one-third. The basic mathematical concepts are briefly touched upon in the beginning which help explain the subsequent development.