  Previous analyses of large databases of Milky Way stars have revealed the
stellar disk of our Galaxy to be warped and that this imparts a strong
signature on the kinematics of stars beyond the solar neighborhood. However,
due to the limitation of accurate distance estimates, many attempts to explore
the extent of these Galactic features have generally been restricted to a
volume near the Sun. By combining Gaia DR2 astrometric solution, StarHorse
distance and stellar abundances from the APOGEE survey, we present the most
detailed and radially expansive study yet of the vertical and radial motions of
stars in the Galactic disk. We map stellar velocity with respect to their
Galactocentric radius, angular momentum, and azimuthal angle and assess their
relation to the warp. A decrease in vertical velocity is discovered at
Galactocentric radius $R=13\ \text{kpc}$ and angular momentum $L_z=2800\
\text{kpc}\ \text{km}\ \text{s}^{-1}$. Smaller ripples in vertical and radial
velocity are also discovered superposed on the main trend. We also discovered
that trends in the vertical velocity with azimuthal angle are not symmetric
about the peak, suggesting the warp to be lopsided. To explain the global trend
in vertical velocity, we built a simple analytical model of the Galactic warp.
Our best fit yields a starting radius of $8.87^{+0.08}_{-0.09}\ \text{kpc}$ and
precession rate of $13.57^{+0.20}_{-0.18}\ \text{km}\ \text{s}^{-1}\
\text{kpc}^{-1}$. These parameters remain consistent across stellar age groups,
a result that supports the notion that the warp is the result of an external,
gravitationally induced phenomenon.

Astrophysics of Galaxies