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On rotational solutions for elliptically excited pendulum

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      Abstract

      The author considers the planar rotational motion of the mathematical pendulum with its pivot oscillating both vertically and horizontally, so the trajectory of the pivot is an ellipse close to a circle. The analysis is based on the exact rotational solutions in the case of circular pivot trajectory and zero gravity. The conditions for existence and stability of such solutions are derived. Assuming that the amplitudes of excitations are not small while the pivot trajectory has small ellipticity the approximate solutions are found both for high and small linear damping. Comparison between approximate and numerical solutions is made for different values of the damping parameter.

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      Most cited references 2

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      Non-trivial effects of high-frequency excitation for strongly damped mechanical systems

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        A generalized perturbed pendulum

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          Author and article information

          Journal
          30 December 2010
          1101.0062
          10.1016/j.physleta.2011.05.021

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Custom metadata
          34D35, 34D20, 34D05, 34E13, 34E05
          16 pages, 5 figures, 1 table
          math-ph math.MP physics.class-ph

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