  % context :The precise and accurate modelling of a terrestrial planet like
Venus is an exciting and challenging topic, all the more interesting since it
can be compared with that of the Earth for which such a modelling has already
been achieved at the milliarcsecond level % aims: We want to complete a
previous study (Cottereau and Souchay, 2009), by determining at the
milliarcsecond level the polhody, i.e. the torque-free motion of the axis of
angular momentum of a rigid Venus in a body-fixed frame, as well as the
nutation of its third axis of figure in space, which is fundamental from an
observational point of view. results :In a first part we have computed the
polhody, i.e. the respective free rotational motion of the axis of angular
momentum of Venus with respect to a body-fixed frame. We have shown that this
motion is highly elliptical, with a very long period of 525 cy to be compared
with 430 d for the Earth. This is due to the very small dynamical flattening of
Venus in comparison with our planet. In a second part we have computed
precisely the Oppolzer terms which allow to represent the motion in space of
the third Venus figure axis with respect to Venus angular momentum axis, under
the influence of the solar gravitational torque. We have determined the
corresponding tables of coefficients of nutation of the third figure axis both
in longitude and in obliquity due to the Sun, which are of the same order of
amplitude as for the Earth. We have shown that the coefficients of nutation for
the third figure axis are significantly different from those of the angular
momentum axis on the contrary of the Earth. Our analytical results have been
validated by a numerical integration which revealed the indirect planetary
effects.
