2002/12/22 by Holger R. Dullin, H. R. Dullin, Andrea Giacobbe +3 · 2 citations
Engineering · Physics and Astronomy · #Control and Dynamics of Mobile Robots #Experimental and Theoretical Physics Studies #Quantum chaos and dynamical systems #nlin.SI
paper · pdf · doi:10.1016/j.physd.2003.10.004
published as Physica D, 190:15--37, 2004. · 30 pages, 5 figures
arxiv created 2002/12/22 · openalex publication_date 2003/12/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.