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Monodromy in the resonant swing spring | | H. R. Dullin
; A. Giacobbe
; R. Cushman
; | | Date: |
22 Dec 2002 | | Journal: | Physica D, 190:15--37, 2004. DOI: 10.1016/j.physd.2003.10.004 | | Subject: | Exactly Solvable and Integrable Systems | nlin.SI | | Abstract: | 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. | | Source: | arXiv, nlin.SI/0212048 | | Services: | Forum | Review | PDF | Favorites | |
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