A Study of the Orbits of the Logarithmic Potential for Galaxies
  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.
