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

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 ste...

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Bibliographic Details
Published inPhysical review letters Vol. 103; no. 3; p. 034301
Main Authors Fitch, N J, Weidner, C A, Parazzoli, L P, Dullin, H R, Lewandowski, H J
Format Journal Article
LanguageEnglish
Published United States 17.07.2009
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Summary: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.
ISSN:0031-9007
DOI:10.1103/PhysRevLett.103.034301