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 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.
Fitch
N J
NJ
JILA and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA.
Weidner
C A
CA
Parazzoli
L P
LP
Dullin
H R
HR
Lewandowski
H J
HJ