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

TL;DR

This paper reports the first experimental observation of Hamiltonian monodromy in a classical elastic pendulum, demonstrating how the system's precession behavior is multivalued and linked to its constants of motion.

Contribution

It provides the first experimental demonstration of classical Hamiltonian monodromy using a resonant elastic pendulum system.

Findings

Observed stepwise precession linked to monodromy

Confirmed multivalued relationship between precession and constants of motion

Demonstrated classical monodromy experimentally

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.