  Internal dissipation in a tidally perturbed librating body differs from the
tidal dissipation in a steadily spinning rotator. First, libration changes the
spectral distribution of tidal damping across the tidal modes, as compared to
the case of steady spin. This changes both the tidal heating rate and the tidal
torque. Second, while a non-librating rotator experiences alternating
deformation only due to the potential force exerted on it by the perturber, a
librating body is also subject to a toroidal force proportional to the angular
acceleration. Third, while the centrifugal force in a steadily spinning body
renders only a permanent deformation, in a librating body this force contains
two 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 terrestrial
body performing small-amplitude libration in longitude. This formalism
incorporates a linear rheological law defining the response of the material to
forcing. While the formalism can work with an arbitrary linear rheology, we
consider a simple example of a Maxwell material.
  We show that, independent of rheology, the forced libration in longitude can
provide a considerable and even leading input in the tidal heating. Based on
the 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 have
participated in the early heating up of some moons. As one possibility, a moon
could have been chipped by collisions $-$ whereby it acquired a higher
triaxiality and a higher forced-libration magnitude and, consequently, a higher
heating rate. After the moon warms up, its triaxiality reduces, and so does the
tidal heating.
