A Study of the Orbits of the Logarithmic Potential for Galaxies

Authors

Sree Ram Valluri, University of Western OntarioFollow
Paul Wiegert, University of Western OntarioFollow
John Drozd, University of Western OntarioFollow
Matt DaSilva, University of Western OntarioFollow

Document Type

Article

Publication Date

Fall 10-27-2011

Journal

Monthly Notices of the Royal Astronomical Society

Volume

427

URL with Digital Object Identifier

10.1111/j.1365-2966.2012.22071.x

Abstract

The logarithmic potential is of great interest and relevance in the study of the dynamics of galaxies. Some small corrections to the work of Contopoulos & Seimenis (1990) who used the method of Prendergast (1982) to find periodic orbits and bifurca- tions within such a potential are presented. The solution of the orbital radial equation for the purely radial logarithmic potential is then considered using the p-ellipse (pre- cessing ellipse) method pioneered by Struck (2006). This differential orbital equation is a special case of the generalized Burgers equation. The apsidal angle is also deter- mined, both numerically as well as analytically by means of the Lambert W and the Polylogarithm functions. The use of these functions in computing the gravitational lensing produced by logarithmic potentials is discussed.

Notes

DOI: 10.1111/j.1365-2966.2012.22071.x

Citation of this paper:

S.R. Valluri, P. Wiegert, J. Drozd and M. DaSilva, “The study of the orbits of logarithmic potentials for galaxies”, Monthly Notices of the Royal Astronomical Society 427 (Oct 2012).