Small Perturbations in Flat Galaxies. II: Time-Dependent Azimuthal Perturbations

Details Small Perturbations in Flat Galaxies. II: Time-Dependent Azimuthal Perturbations Small Perturbations in Flat Galaxies. II: Time-Dependent Azimuthal Perturbations

Mar 1973

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1973ap%26ss..21...79c&link_type=abstract

Analytical Procedures for Eclipsing Binary Light Curves, Proceedings of IAU Colloq. 16, held in Philadelphia, PA, September, 197

Statistics

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Scientific paper

This paper describes methods of calculating the response of a flat galaxy of stars to a perturbation which can depend on time and on angle. The starting point is the response to a pulse: the response to any other time dependence can be found by convolution. A single orbit responds with growing oscillations at the resonant frequencies, so the Laplace transform of the orbital response has a set of double poles along the real frequency axis. The problem of finding the response of the system is the problem of integrating these poles over all orbits. A simple expression for the orbital response is found in terms of the derivatives of Hankel-Laguerre functions with respect to action-angle variables. These derivatives can be computed with the aid of the computationally convenient variables introduced in Paper I. The Laplace transform of the system response is expanded in a series of simple basis functions. The expansion coefficients are found as integrals over all orbits of the basis functions multipled by the amplitudes of the orbital response at the resonant frequencies. The integrands are not singular, and the integration is straightforward.

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