Dynamics of the pendulum with periodically varying length |
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Authors: | Anton O Belyakov Alexander P Seyranian |
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Institution: | a Institute of Mechanics, Moscow State Lomonosov University, Michurinsky pr. 1, Moscow 119192, Russia b DISAT, Universita di L’Aquila, P. le Pontieri, Monteluco Roio 1, L’Aquila 67040, Italy |
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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 a 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 a numerical study. Chaotic motions of the pendulum depending on problem parameters are investigated numerically. |
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Keywords: | Pendulum of variable length Regular rotation Tumbling chaos Averaging method Stability of limit cycle Quasi-linear oscillatory system |
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