  Trajectories in logarithmic potentials are investigated by taking as example
the motion of an electron within a cylindrical capacitor. The solution of the
equation of motion in plane polar coordinates, (r,{\phi}) is attained by
forming a series expansion of r and of 1/r as a function of {\phi}. The terms
of the series contain polynomials, the recurrence relation of which is given,
together with some further characteristics. By the comparison-theorem of
infinite series, the convergence of the solution is demonstraded. The simplest
trajectories in logarithmic potentials are represented by rosette type orbits
with a period of 4{\pi}/3, and by circular paths.
