Zobrazeno 1 - 10
of 68
pro vyhledávání: '"Polekhin, Ivan"'
Autor:
Polekhin, Ivan
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 the pendulum is zero and there is no friction in the system. We show t
Externí odkaz:
http://arxiv.org/abs/2209.03724
Autor:
Polekhin, Ivan
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 rapidly oscillating. We assume that the pivot point of the pendulum rapid
Externí odkaz:
http://arxiv.org/abs/2205.12057
Autor:
Polekhin, Ivan
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 field. We do not assume that this force field is weak or rapidly oscil
Externí odkaz:
http://arxiv.org/abs/2105.11980
Autor:
Kozlov, Valery, Polekhin, Ivan
In the paper, we study the dynamics of planar $n$-gons, which can be considered as discrete models of threads. The main result of the paper is that, under some weak assumptions, these systems are not integrable in the sense of Liouville. This holds f
Externí odkaz:
http://arxiv.org/abs/2009.09517
Autor:
Polekhin, Ivan
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 force field. We study the existence of forced oscillations in the system.
Externí odkaz:
http://arxiv.org/abs/2006.03406
Autor:
Polekhin, Ivan
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 forced oscillations in such systems and study the asymptotic behaviour of s
Externí odkaz:
http://arxiv.org/abs/1912.04626
Autor:
Polekhin, Ivan
In the paper we study the existence of a forced oscillation in two Lagrange systems with gyroscopic forces: a spherical pendulum in a magnetic field and a point on a rotating closed convex surface. We show how it is possible to prove the existence of
Externí odkaz:
http://arxiv.org/abs/1912.04076
Autor:
Polekhin, Ivan
We consider a possible application of the Wa\.zewski topological method to feedback control systems and to more general dynamical systems. We show how this method can be used to prove the impossibility of global stabilization in such problems. Moreov
Externí odkaz:
http://arxiv.org/abs/1912.04027
Autor:
Polekhin, Ivan
We present sufficient conditions for the existence of forced oscillations in non-autonomous mechanical systems. Previously, similar results were obtained for systems with friction. Presented results hold both for systems with and without friction. So
Externí odkaz:
http://arxiv.org/abs/1912.03987
Autor:
Polekhin, Ivan
The change of the precession angle is studied analytically and numerically for the integrable tops of Kovalevskaya and Goryachev-Chaplygin. Based on the known results on the topology of Liouville foliations for these systems, we find initial conditio
Externí odkaz:
http://arxiv.org/abs/1807.09016