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On Nonlinear Dynamics of the Pendulum with Periodically Varying Length

By Anton O. Belyakov and Alexander P. Seyranian

Abstract

Dynamic behavior of a weightless rod with a point mass sliding along the rod axis according to periodic law is studied. This is the pendulum with periodically varying length which is also treated as a simple model of child's swing. Asymptotic expressions for boundaries of instability domains near resonance frequencies are derived. Domains for oscillation, rotation, and oscillation-rotation motions in parameter space are found analytically and compared with numerical study. Two types of transitions to chaos of the pendulum depending on problem parameters are investigated numerically.Comment: 8 pages, 8 figure

Topics: Mathematical Physics, 34E99, 34D35, 37D45, 34D45
Publisher: 'Elsevier BV'
Year: 2009
DOI identifier: 10.1016/j.physd.2009.04.015
OAI identifier: oai:arXiv.org:0910.3802

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