Physics and Astronomy Publications

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


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