Premium
Bifurcation of slow motions in a stiff spring pendulum
Author(s) -
Steindl Alois
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010341
Subject(s) - double pendulum , kapitza's pendulum , pendulum , bifurcation , spring (device) , physics , classical mechanics , mechanics , orbit (dynamics) , dynamics (music) , stiffness , inverted pendulum , symmetry (geometry) , mathematics , nonlinear system , geometry , engineering , thermodynamics , quantum mechanics , acoustics , aerospace engineering
We consider free oscillations of a double pendulum, where one of the pendula is modelled as a very stiff spring. Contrary to a single spring pendulum numerical simulations show an unexpected large influence of the fast longitudinal oscillations on the slow pendulum oscillations even for extremely large values of the stiffness. The transition from the regular motion, which is governed by the dynamics of a rigid double pendulum close to a periodic orbit, to the irregular motion with large contributions from the longitudinal oscillations occurs due to a subcritical symmetry breaking bifurcation of the periodic solution. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)