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Download fileMonodromy in the resonant swing spring
preprint
posted on 2005-07-29, 14:41 authored by Holger R. Dullin, Andrea Giacobbe, Richard CushmanThis 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.
History
School
- Science
Department
- Mathematical Sciences
Pages
356402 bytesPublication date
2003Notes
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.Language
- en