Title: Rotation of a synchronous viscoelastic shell,
Abstract: Several natural satellites of the giant planets have shown evidence of a
global internal ocean, coated by a thin, icy crust. This crust is probably
viscoelastic, which would alter its rotational response. This response would
translate into several rotational quantities, i.e. the obliquity, and the
librations at different frequencies, for which the crustal elasticity reacts
differently. This study aims at modelling the global response of the
viscoelastic crust. For that, I derive the time-dependency of the tensor of
inertia, which I combine with the time evolution of the rotational quantities,
thanks to an iterative algorithm. This algorithm combines numerical simulations
of the rotation with a digital filtering of the resulting tensor of inertia.
The algorithm works very well in the elastic case, provided the problem is not
resonant. However, considering tidal dissipation adds different phase lags to
the oscillating contributions, which challenge the convergence of the
algorithm.