Trajectories in Logarithmic Potentials
General Physics
2010-09-03 v1 Classical Physics
Abstract
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.
Keywords
Cite
@article{arxiv.1009.0422,
title = {Trajectories in Logarithmic Potentials},
author = {Erwin A. T. Wosch},
journal= {arXiv preprint arXiv:1009.0422},
year = {2010}
}
Comments
17 pages, 5 figures