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Monodromy in the resonant swing spring

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posted on 2005-07-29, 14:41 authored by Holger R. Dullin, Andrea Giacobbe, Richard Cushman
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.



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This pre-print has been submitted, and accepted, to the journal, Physica D - Nonlinear Phenomena [© Elsevier]. The definitive version: DULLIN, H.R., GIACOBBE, A. and CUSHMAN, R., 2004. Monodromy in the resonant swing spring. Physica D - Nonlinear Phenomena, 190(1-2), pp. 15-37, is available at: http://www.sciencedirect.com/science/journal/01672789.


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