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Complex trajectories of a simple pendulum. (English) Zbl 1112.70020
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 $\mathrm{𝒫𝒯}$-symmetric. The classical motion for this $\mathrm{𝒫𝒯}$-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:
 70K55 Transition to stochasticity (chaotic behavior) 70K40 Forced nonlinear motions (general mechanics)
##### Keywords:
complex chaotic motion; periodic forcing term