Monodromy in the resonant swing spring

In this paper, it is shown 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(χ + iλ), where χ and λ are functions of the integrals. The resonant swing spring is therefore a system where monodromy has easily observed physical consequences.