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arXiv · 1407.1688

A new method for the determination of action integrals in the study of galactic dynamics

Michael F. J. Fox
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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.

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Michael F. J. Fox. 2014-07-07. A new method for the determination of action integrals in the study of galactic dynamics. https://arxiv.org/abs/1407.1688

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