Monodromy in the resonant swing spring

Dullin, H. R.; Giacobbe, A.; Cushman, R.

Monodromy in the resonant swing spring

Authors

Dullin, H. R.

Giacobbe, A.

Cushman, R.

Description

This paper shows that an integrable approximation of the spring pendulum, when tuned to be in $1:1:2$ resonance, has monodromy. The stepwise precession angle of the swing plane of the resonant spring pendulum is shown to be a rotation number of the integrable approximation. Due to the monodromy, this rotation number is not a globally defined function of the integrals. In fact at lowest order it is given by $\arg(a+ib)$ where $a$ and $b$ are functions of the integrals. The resonant swing spring is therefore a system where monodromy has easily observed physical consequences.
30 pages, 5 figures