  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.
