Complex trajectories of a simple pendulum

Carl M Bender, Darryl D Holm, Daniel W Hook
2006 Journal of Physics A: Mathematical and Theoretical  
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.
doi:10.1088/1751-8113/40/3/f01 fatcat:qnbzt6xe7ngtzdneev2zd2wxqu