Complex Trajectories of a Simple Pendulum
arXiv:math-ph/0609068 · doi:10.1088/1751-8113/40/3/F01
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.
11 pages, 12 figures