  The rotation and orientation of Mars is commonly described using two
different sets of angles, namely the Euler angles wrt the Mars orbit plane and
the right ascension, declination, and prime meridian location angles wrt the
Earth equator at J2000 (as adopted by the IAU). We propose a formulation for
both these sets of angles, which consists of the sum of a second degree
polynomial and of periodic and Poisson series. Such a formulation is shown here
to enable accurate (and physically sound) transformation from one set of angles
to the other. The transformation formulas are provided and discussed in this
paper. In particular, we point that the quadratic and Poisson terms are key
ingredients to reach a transformation precision of 0.1 mas, even 30 years away
from the reference epoch of the rotation model (e.g. J2000). Such a precision
is required to accurately determine the smaller and smaller geophysical signals
observed in the high-accuracy data acquired from the surface of Mars. In
addition, we present good practices to build an accurate Martian rotation model
over a long time span (30 years around J2000) or over a shorter one (e.g.
lifetime of a space mission). We recommend to consider the J2000 mean orbit of
Mars as the reference plane for Euler angles. An accurate rotation model should
make use of up-to-date models for the rigid and liquid nutations, relativistic
corrections in rotation, and polar motion induced by the external torque. Our
transformation model and recommendations can be used to define the future IAU
solution for the rotation and orientation of Mars using right ascension,
declination, and prime meridian location. In particular, thanks to its
quadratic terms, our transformation model does not introduce arbitrary and
non-physical terms of very long period and large amplitudes, thus providing
unbiased values of the rates and epoch values of the angles.
