A review of action estimation methods for galactic dynamics
  We review the available methods for estimating actions, angles and
frequencies of orbits in both axisymmetric and triaxial potentials. The methods
are separated into two classes. Unless an orbit has been trapped by a
resonance, convergent, or iterative, methods are able to recover the actions to
arbitrarily high accuracy given sufficient computing time. Faster
non-convergent methods rely on the potential being sufficiently close to a
separable potential and the accuracy of the action estimate cannot be improved
through further computation. We critically compare the accuracy of the methods
and the required computation time for a range of orbits in an axisymmetric
multi-component Galactic potential. We introduce a new method for estimating
actions that builds on the adiabatic approximation of Sch\"onich & Binney
(2012) and discuss the accuracy required for the actions, angles and
frequencies using suitable distribution functions for the thin and thick discs,
the stellar halo and a star stream. We conclude that for studies of the disc
and smooth halo component of the Milky Way the most suitable compromise between
speed and accuracy is the St\"ackel Fudge, whilst when studying streams the
non-convergent methods do not offer sufficient accuracy and the most suitable
method is computing the actions from an orbit integration via a generating
function. All the software used in this study can be downloaded from
https://github.com/jls713/tact.
