Dullin, Holger and Giacobbe, Andrea and Cushman, Richard (2004) Monodromy in the resonant swing spring. [Journal papers (printed)]
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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(a + i b), where a and b are functions of the integrals. The resonant swing
spring is therefore a system where monodromy has easily observed physical consequences.
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