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arXiv · 1209.1342

A Study of the Orbits of the Logarithmic Potential for Galaxies

S. R. Valluri·P. A. Wiegert·J. Drozd·M. DaSilva
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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 bifurcations 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 (precessing ellipse) method pioneered by Struck (2006). This differential orbital equation is a special case of the generalized Burgers equation. The apsidal angle is also determined, 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.

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S. R. Valluri, P. A. Wiegert, J. Drozd, M. DaSilva. 2012-09-06. A Study of the Orbits of the Logarithmic Potential for Galaxies. https://doi.org/10.1111/j.1365-2966.2012.22071.x

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