A new method for the determination of action integrals in the study of galactic dynamics
Abstract
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.
Keywords
Cite
@article{arxiv.1407.1688,
title = {A new method for the determination of action integrals in the study of galactic dynamics},
author = {Michael F. J. Fox},
journal= {arXiv preprint arXiv:1407.1688},
year = {2014}
}
Comments
Masters Thesis, University of Oxford, 17 pages, 7 figures