The power of co-ordinate transformations in dynamical interpretations of
  Galactic structure
  $Gaia$ DR2 has provided an unprecedented wealth of information about the
positions and motions of stars in our Galaxy, and has highlighted the degree of
disequilibria in the disc. As we collect data over a wider area of the disc it
becomes increasingly appealing to start analysing stellar actions and angles,
which specifically label orbit space, instead of their current phase space
location. Conceptually, while $\bar{x}$ and $\bar{v}$ tell us about the
potential and local interactions, grouping in action puts together stars that
have similar frequencies and hence similar responses to dynamical effects
occurring over several orbits. Grouping in actions and angles refines this
further to isolate stars which are travelling together through space and hence
have shared histories. Mixing these coordinate systems can confuse the
interpretation. For example, it has been suggested that by moving stars to
their guiding radius, the Milky Way spiral structure is visible as ridge-like
overdensities in the $Gaia$ data \citep{Khoperskov+19b}. However, in this work,
we show that these features are in fact the known kinematic moving groups, both
in the $L_z-\phi$ and the $v_{\mathrm{R}}-v_{\phi}$ planes. Using simulations
we show how this distinction will become even more important as we move to a
global view of the Milky Way. As an example, we show that the radial velocity
wave seen in the Galactic disc in $Gaia$ and APOGEE should become stronger in
the action-angle frame, and that it can be reproduced by transient spiral
structure.
