  For the first time, we determine the complete spin- and momentum-dependent
order v^2 corrections to the static interquark potential from simulations of
QCD in the valence quark approximation at inverse lattice spacings of 2-3 GeV.
A new flavor dependent correction to the central potential is found. We report
a 1/r^2 contribution to the long range spin-orbit potential V_1'. The other
spin-dependent potentials turn out to be short ranged and can be well
understood by means of perturbation theory. The momentum-dependent potentials
qualitatively agree with minimal area law expectations. In view of spectrum
calculations, we discuss the matching of the effective nonrelativistic theory
to QCD as well as renormalization of lattice results. In a first survey of the
resulting bottomonia and charmonia spectra we reproduce the experimental levels
within average errors of 12.5 MeV and 22 MeV, respectively.
