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arXiv · 0906.2941

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

Noah J. Fitch·Carrie A. Weidner·L. Paul Parazzoli·H. R. Dullin·Heather J. Lewandowski
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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.

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Noah J. Fitch, Carrie A. Weidner, L. Paul Parazzoli, H. R. Dullin, Heather J. Lewandowski. 2009-06-16. Experimental demonstration of classical Hamiltonian monodromy in the 1:1:2 resonant elastic pendulum. https://doi.org/10.1103/physrevlett.103.034301

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