8 citations · 28 across the 15 of their papers we have counts for
17 papers
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…
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…
The Spherical Kapitza-Whitney Pendulum
Ivan Polekhin
In this paper we study the global dynamics of the inverted spherical pendulum with a vertically vibrating suspension point in the presence of an external horizontal periodic force…
On the non-integrability and dynamics of discrete models of threads
Valery Kozlov, Ivan Polekhin
In the paper, we study the dynamics of planar -gons, which can be considered as discrete models of threads. The main result of the paper is that, under some weak assumptions, th…
The method of averaging for the Kapitza-Whitney pendulum
Ivan Polekhin
A generalization of the classical Kapitza pendulum is considered: an inverted planar mathematical pendulum with a vertically vibrating pivot point in a time-periodic horizontal for…
Averaging method and asymptotic solutions in some mechanical problems
Ivan Polekhin
In the paper we consider systems in oscillating force fields such that the classical method of averaging can be applied. We present sufficient conditions for the existence of force…