  We present models for a heteronuclear diatomic molecular ion in a linear Paul
trap in a rigid-rotor approximation, one purely classical, the other where the
center-of-mass motion is treated classically while rotational motion is
quantized. We study the rotational dynamics and their influence on the motion
of the center-of-mass, in the presence of the coupling between the permanent
dipole moment of the ion and the trapping electric field. We show that the
presence of the permanent dipole moment affects the trajectory of the ion, and
that it departs from the Mathieu equation solution found for atomic ions. For
the case of quantum rotations, we also evidence the effect of the
above-mentioned coupling on the rotational states of the ion.
