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A. Belyakov:
"Rotational solutions for elliptically excited pendulum";
in: "5th International Conference on Physics and Control (PhysCon 2011) September 5-8, 2011, León, Spain", herausgegeben von: The Laboratory "Control of Complex Systems", IPME RAS; IPACS Electronic library, 2011, 7 S.

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 ex-
istence and stability of such solutions are derived. As-
suming that the amplitudes of excitations are not small
while the pivot trajectory has small ellipticity the ap-
proximate 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.

elliptically excited pendulum; parametric pendulum; unbalanced rotor; asymptotic methods