  We present the chemodynamic structure of the solar neighbourhood using 62 814
stars within a 500 pc sphere of the Sun observed by GALAH and with astrometric
parameters from Gaia DR2. We measure the velocity dispersion for all three
components (vertical, radial, and tangential) and find that it varies smoothly
with [Fe/H] and [$\alpha$/Fe] for each component. The vertical component is
especially clean, with $\sigma_{v_z}$ increasing from a low of $8$ km s$^{-1}$
at solar-[$\alpha$/Fe] and [Fe/H] to a high of more than 50 km s$^{-1}$ for
more metal-poor and [$\alpha$/Fe] enhanced populations. We find no evidence of
a large decrease in the velocity dispersion of the higher-[$\alpha$/Fe]
populations as claimed in analysis prior to Gaia DR2, although the trend of
increasing velocity dispersion with [$\alpha$/Fe] for the same metallicity does
significantly flatten at high-[$\alpha$/Fe]. The eccentricity distribution for
local stars varies most strongly as a function of [$\alpha$/Fe], where stars
with [$\alpha$/Fe]$<0.1$ dex having generally circular orbits ($e<0.15$), while
the median eccentricity increases rapidly for more [$\alpha$/Fe]-enhanced
stellar populations up to $e\sim0.35$. These [$\alpha$/Fe]-enhanced populations
have guiding radii consistent with origins in the inner Galaxy. Of the stars
with metallicities much higher than the local ISM ([Fe/H]>0.1 dex), we find
that more than 70\% have $e<0.2$ and are likely observed in the solar
neighbourhood through churning/migration rather than blurring effects, as the
epicyclic motion for these stars is not large enough to reach the radii at
which they were likely born based on their metallicity.
