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Experimental Demonstration of Classical Hamiltonian Monodromy in the 112 Resonant Elastic Pendulum

N. J. Fitch, C. A. Weidner, L. P. Parazzoli, H. R. Dullin, and H. J. Lewandowski
Phys. Rev. Lett. 103, 034301 – Published 15 July 2009
Physics logo See Synopsis: Swinging and springing

Abstract

The 112 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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  • Received 7 April 2009

DOI:https://doi.org/10.1103/PhysRevLett.103.034301

©2009 American Physical Society

Synopsis

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Swinging and springing

Published 27 July 2009

Can physicists still learn anything about molecular motion from the classical pendulum?

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Authors & Affiliations

N. J. Fitch1, C. A. Weidner1, L. P. Parazzoli1, H. R. Dullin2, and H. J. Lewandowski1

  • 1JILA and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440
  • 2School of Mathematics and Statistics, The University of Sydney, Sydney, NSW 2006, Australia

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Issue

Vol. 103, Iss. 3 — 17 July 2009

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