Core-mantle friction induced by the precession of the Moon's spin axis is a strong heat source in the deep lunar mantle during the early phase of a satellite's evolution, but its influence on the long-term thermal evolution still remains poorly explored. Using a one-dimensional thermal evolution model, we show that core-mantle friction can sustain global-scale partial melting in the upper lunar mantle until similar to 3.1 Ga, thus accounting for the intense volcanic activity on the Moon before similar to 3.0 Ga. Besides, core-mantle friction tends to suppress the secular cooling of the lunar core and is unlikely to be an energy source for the long-lived lunar core dynamo. Our model also favours the transition of the Cassini state before the end of the lunar magma ocean phase (similar to 4.2 Ga), which implies a decreasing lunar obliquity over time after the solidification of the lunar magma ocean. Such a trend of lunar obliquity evolution may allow volcanically released water to be buried in the lunar regolith of the polar regions. As a consequence, local water ice could be more abundant than previously thought when considering only its accumulation caused by solar wind and comet spreading. Precession-driven core-mantle friction can maintain a long-lived volcanism on the Moon until similar to 3.1 Ga. Modelling suggests the Cassini state transition before the end of lunar magma ocean phase (similar to 4.2 Ga), which allows a decreasing lunar obliquity over time and the deposition of water ice in the lunar polar regions afterwards.

We here develop, in an angular momentum approach, a consistent model that integrates all rotation variables and considers forcing both by the central planet and a potential atmosphere. Existing angular momentum approaches for studying the polar motion, precession, and libration of synchronously rotating satellites, with or without an internal global fluid layer (e.g., a subsurface ocean) usually focus on one aspect of rotation and neglect coupling with the other rotation phenomena. The model variables chosen correspond most naturally with the free modes, although they differ from those of Earth rotation studies, and facilitate a comparison with existing decoupled rotation models that break the link between the rotation motions. The decoupled models perform well in reproducing the free modes, except for the Free Ocean Nutation in the decoupled polar motion model. We also demonstrate the high accuracy of the analytical forced solutions of decoupled models, which are easier to use to interpret observations from past and future space missions. We show that the effective decoupling between the polar motion and precession implies that the spin precession and its associated mean obliquity are mainly governed by the external gravitational torque by the parent planet, whereas the polar motion of the solid layers is mainly governed by the angular momentum exchanges between the atmosphere (e.g., for Titan) and the surface. To put into perspective the difference between rotation models for a synchronously rotating icy moon with a thin ice shell and classical Earth rotation models, we also consider the case of the Moon, which has a thick outer layer above a liquid core. We also show that for non-synchronous rotators, the free precession of the outer layer in space degenerates into the tilt-over mode.