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.

5 pages, accepted to PRL

References in corpus (2)

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

Cited by in corpus (7)

• Geometric Origin of the Tennis Racket Effect
• Fractional bidromy in the vibrational spectrum of HOCl
• Classical and quantum rotation numbers of asymmetric top molecules
• Monodromy and chaos for condensed bosons in optical lattices
• The height invariant of a four-parameter semitoric system with two focus-focus singularities
• An introduction to classical monodromy: applications to molecules in external fields
• Symplectic theory of completely integrable Hamiltonian systems