Complex trajectories of a simple pendulum

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 -symmetric. The classical motion for this -symmetric Hamiltonian is examined in detail. The complex motion of this pendulum in the presence of an external periodic forcing term is also studied.