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Rotational solutions for elliptically excited pendulum

Anton Belyakov
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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