On a periodically forced, weakly damped pendulum. Part 3: Vertical forcing

DOI10.1017/S0334270000008201zbMath0702.70028MaRDI QIDQ3481243

Peter J. Bryant, J. W. Miles

Publication date: 1990

Published in: The Journal of the Australian Mathematical Society. Series B. Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Mathieu equationchaotic motionregions of stabilityphase-locked solutionsResonance curvessymmetry-breaking, period- doubling sequenceweakly damped pendulum forced

Mathematics Subject Classification ID

Forced motions for nonlinear problems in mechanics (70K40) Bifurcations and instability for nonlinear problems in mechanics (70K50) Vibrations in dynamical problems in solid mechanics (74H45) Dynamical systems and ergodic theory (37-XX)

Related Items

Periodic oscillations and attracting basins for a parametrically excited pendulum, Approximations for period-1 rotation of vertically and horizontally excited parametric pendulum, Rotating periodic orbits of the parametrically excited pendulum, Comparisons between the pendulum with varying length and the pendulum with oscillating support, Symmetry-breaking in the response of the parametrically excited pendulum model, A purely frequency based Floquet-Hill formulation for the efficient stability computation of periodic solutions of ordinary differential systems, The use of manifold tangencies to predict orbits, bifurcations and estimate escape in driven systems.