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Internal dissipation in a tidally perturbed librating body differs from thetidal dissipation in a steadily spinning rotator. First, libration changes thespectral distribution of tidal damping across the tidal modes, as compared tothe case of steady spin. This changes both the tidal heating rate and the tidaltorque. Second, while a non-librating rotator experiences alternatingdeformation only due to the potential force exerted on it by the perturber, alibrating body is also subject to a toroidal force proportional to the angularacceleration. Third, while the centrifugal force in a steadily spinning bodyrenders only a permanent deformation, in a librating body this force containstwo alternating components $-$ one radial, another a degree-2 potential force.Both contribute to heating, as well as to the tidal torque and potential.  We build a formalism to describe dissipation in a homogeneous terrestrialbody performing small-amplitude libration in longitude. This formalismincorporates a linear rheological law defining the response of the material toforcing. While the formalism can work with an arbitrary linear rheology, weconsider a simple example of a Maxwell material.  We show that, independent of rheology, the forced libration in longitude canprovide a considerable and even leading input in the tidal heating. Based onthe observed parameters, this input amounts to 52% in Phobos, 33% in Mimas, 23%in Enceladus, and 96% in Epimetheus. This supports the hypothesis by Makarov &Efroimsky (2014) that the additional damping due to forced libration may haveparticipated in the early heating up of some moons. As one possibility, a mooncould have been chipped by collisions $-$ whereby it acquired a highertriaxiality and a higher forced-libration magnitude and, consequently, a higherheating rate. After the moon warms up, its triaxiality reduces, and so does thetidal heating.

Dissipation in a tidally perturbed body librating in longitude