  We consider the dynamic nuclear spin polarization (DNP) using two electrons
in a double quantum dot in presence of external magnetic field and spin-orbit
interaction, in various schemes of periodically repeated sweeps through the
S-T+ avoided crossing. By treating the problem semi-classically, we find that
generally the DNP have two distinct contributions - a geometrical polarization
and a dynamic polarization, which have different dependence on the control
parameters such as the sweep rates and waiting times in each period. Both terms
show non-trivial dependence on those control parameter. We find that even for
small spin-orbit term, the dynamical polarization dominates the DNP in presence
of a long waiting period near the S-T+ avoided crossing, of the order of the
nuclear Larmor precession periods. A detailed numerical analysis of a specific
control regime can explain the oscillations observed by Foletti et.~al.~in
arXiv:0801.3613.
