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Zbl 1112.70020
Bender, Carl M.; Holm, Darryl D.; Hook, Daniel W.
Complex trajectories of a simple pendulum. (English)
[J] J. Phys. A, Math. Theor. 40, No. 3, F81-F89 (2007). ISSN 1751-8113; ISSN 1751-8121/e

Summary: 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 $\mathcal{PT}$-symmetric. The classical motion for this $\mathcal{PT}$-symmetric Hamiltonian is examined in detail. We also study the complex motion of this pendulum in the presence of an external periodic forcing term.

MSC 2000:: *70K55 Transition to stochasticity (chaotic behavior)
70K40 Forced motions (general mechanics)

Keywords: complex chaotic motion; periodic forcing term

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Zentralblatt MATH Berlin [Germany]