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math.DS2022★ 1 cited
On the dynamics and integrability of the Ziegler pendulum
Ivan Polekhin
We prove that the Ziegler pendulum -- a double pendulum with a follower force -- can be integrable, provided that the stiffness of the elastic spring located at the pivot point of…
math.DS2022
Asymptotically Stable Non-Falling Solutions of the Kapitza-Whitney Pendulum
Ivan Polekhin
The planar inverted pendulum with a vibrating pivot point in the presence of an additional horizontal force field is studied. The horizontal force is not assumed to be small or rap…