Complex Trajectories of a Simple Pendulum
Mathematical Physics
2011-07-19 v1 High Energy Physics - Theory
math.MP
Chaotic Dynamics
Abstract
The motion of a classical pendulum in a gravitational field of strength g is explored. The complex trajectories as well as the real ones are determined. If g is taken to be imaginary, the Hamiltonian that describes the pendulum becomes PT-symmetric. The classical motion for this PT-symmetric Hamiltonian is examined in detail. The complex motion of this pendulum in the presence of an external periodic forcing term is also studied.
Cite
@article{arxiv.math-ph/0609068,
title = {Complex Trajectories of a Simple Pendulum},
author = {Carl M. Bender and Darryl D. Holm and Daniel W. Hook},
journal= {arXiv preprint arXiv:math-ph/0609068},
year = {2011}
}
Comments
11 pages, 12 figures