8 citations · 8 across the 3 of their papers we have counts for
6 papers
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…
Remarks on forced oscillations in some systems with gyroscopic forces
Ivan Polekhin
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 close…
Some results on the existence of forced oscillations in mechanical systems
Ivan Polekhin
We present sufficient conditions for the existence of forced oscillations in non-autonomous mechanical systems. Previously, similar results were obtained for systems with friction.…
Precession of the Kovalevskaya and Goryachev-Chaplygin tops
Ivan Polekhin
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 topolo…
On motions without falling of an inverted pendulum with dry friction
Ivan Polekhin
An inverted planar pendulum with horizontally moving pivot point is considered. It is assumed that the law of motion of the pivot point is given and the pendulum is moving in the p…