Experimental demonstration of classical Hamiltonian monodromy in the 1:1:2 resonant elastic pendulum

Abstract

The 1:1:2 resonant elastic pendulum is a simple classical system that displays the phenomenon known as Hamiltonian monodromy. With suitable initial conditions, the system oscillates between nearly pure springing and nearly pure elliptical-swinging motions, with sequential major axes displaying a stepwise precession. The physical consequence of monodromy is that this stepwise precession is given by a smooth but multivalued function of the constants of motion. We experimentally explore this multivalued behavior. To our knowledge, this is the first experimental demonstration of classical monodromy.

arXiv comment5 pages, accepted to PRL

References in corpus (2)

• Stepwise Precession of the Resonant Swinging Spring
• Monodromy in the resonant swing spring

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• Symplectic theory of completely integrable Hamiltonian systems