  Although the rotation of some Saturn's satellites in spin-orbit has already
been studied by several authors, this is not the case of the rotation of
Phoebe, which has the particularity of being non resonant. The purpose of the
paper is to determine for the first time and with precision its
precession-nutation motion. We adopt an Hamiltonian formalism of the motion of
rotation of rigid celestial body set up by Kinoshita (1977) based on Andoyer
variables and canonical equations. First we calculate Phoebe's obliquity at
J2000,0 from available astronomical data as well as the gravitational
perturbation due to Saturn on Phoebe rotational motion. Then we carry out a
numerical integration and we compare our results for the precession rate and
the nutation coefficients with pure analytical model. Our results for Phoebe
obliquity (23{\deg}95) and Phoebe precession rate (5580".65/cy) are very close
to the respective values for the Earth. Moreover the amplitudes of the
nutations (26" peak to peak for the nutaton in longitude and 8" for the
nutation in obliquity) are of the same order as the respective amplitudes for
the Earth. We give complete tables of nutation, obtained from a FFT analysis
starting from the numerical signals. We show that a pure analytical model of
the nutation is not accurate due to the fact that Phoebe orbital elements e, M
and Ls are far from having a simple linear behaviour. The precession and
nutation of Phoebe have been calculated for the first time in this paper. We
should keep on the study in the future by studying the additional gravitational
effects of the Sun, of the large satellites as Titan, as well as Saturn
dynamical ellipticity.
