A new method for the determination of action integrals in the study of
  galactic dynamics
  Action-angle coordinates are an essential tool for understanding the
properties of the six dimensional phase space involved in orbits of stars in
galactic potentials. A new method, which does not require specific knowledge of
a generating function, is described, implemented and tested that calculates the
actions of an orbit in an arbitrary potential of an integrable Hamiltonian
given a set of Cartesian phase space points. The method chooses between the
simple harmonic oscillator and isochrone potentials to fit the data using a
Levenberg-Marquardt routine. An average is taken over the angle coordinates by
calculating volumes in phase space using the metric free FiEstAS algorithm. The
perfect ellipsoidal potential, with actions chosen a priori, is used to test
the output of the algorithm, giving some results that agree within 1%.
Minimisation of a sampling error is discussed along with an identification of a
source of noise in the data.
