Sergei V. Sokolov

Moscow Institute of Physics and Technology | MIPT · Department of Theoretical Mechanics

The article considers a model system that describes a dynamically symmetric rigid body in the Lagrange case with a suspension point that performs high-frequency oscillations. This system, reduced to axes rigidly connected to the body, after the averaging procedure, has the form of the Hamilton equations with two degrees of freedom and has the Liouv...

This paper is concerned with a system of two vortex filaments in a Bose-Einstein condensate enclosed in a harmonic trap. Such a problem is a restriction for the more complicated case of a circular cylinder rigid body and two rectilinear vortex filaments. For these conditions we propose that rigid body has a infinitely big mass. Here we present the...

We study a mechanical system that consists of a 2D rigid body interacting dynamically with two point vortices in an unbounded volume of an incompressible, otherwise vortex-free, perfect fluid. The system has four degrees of freedom. The governing equations can be written in Hamiltonian form, are invariant under the action of the group \(E(2)\) and...

The goal of this report is to determine and analyze the bifurcation diagram of the one model of a Lagrange top with a vibrating suspension point

We consider plane-parallel motion of a circular cylinder interacting dynamically with two point vortices. The system has 4 degrees of freedom and is governed by a set of ordinary differential equations which prove to be Hamiltonian. The governing equations are invariant under rigid transformations of the plane and thus admit three additional integr...

Completely Liouville integrable Hamiltonian system with two degrees of freedom is considered. This Hamiltonian system describes the dynamics of two vortex filaments in a Bose-Einstein condensate enclosed in a cylindrical trap and dynamics of two vortices in the ideal fluid contained in a domain with the form of a circular cylinder, generatrix of wh...

Completely Liouville integrable Hamiltonian system with two degrees of freedom, de- scribing the dynamics of two vortex filaments in a Bose – Einstein condensate enclosed in a cylindrical trap, is considered. For the system of two vortices with identical intensities detected bifurcation of three Liouville tori into one. Such a bifurcation was found...

Completely Liouville integrable Hamiltonian system with two degrees of freedom, describing the dynamics of two vortex filaments in a Bose-Einstein condensate enclosed in a cylindrical trap, is considered. For the system of two vortices with identical intensities detected bifurcation of three Liouville tori into one. Such a bifurcation was found in...

This paper deals with the problem of motion of a system of two point vortices in a Bose–Einstein condensate enclosed in a cylindrical trap. Bifurcation diagram is analytically determined for the intensities of one sign and bifurcations of Liouville tori are investigated. We obtain explicit formulas for determining the type of critical trajectories,...

The following sentence should be added to the section ACKNOWLEDGMENTS: This work was partially supported by the grants of Russian Foundation for Basic Research nos. 16-01-00170 and 16-01-00809.

A high-amplitude microwave magnetic field localized at the nanoscale is a desirable tool for various applications within the rapidly developing field of nanomagnetism. Here, we drive magnetization precession by coherent phonons in a metal ferromagnetic nanograting and generate ac-magnetic induction with extremely high amplitude (up to $10$ mT) and...

In this paper new invariant relations for one critical subsystem of a completely integrable Hamiltonian system with three degrees of freedom found by V.V. Sokolov and A.V. Tsyganov, known as a generalized two-field gyrostat, are obtained. The dynamic system that is induced on the invariant four-dimensional submanifolds is almost everywhere Hamilton...

This paper is concerned with a system two point vortices in a Bose–Einstein condensate enclosed in a trap. The Hamiltonian form of equations of motion is presented and its Liouville integrability is shown. A bifurcation diagram is constructed, analysis of bifurcations of Liouville tori is carried out for the case of opposite-signed vortices, and th...

The case of motion of a generalized two-field gyrostat found by V. V. Sokolov and A.V. Tsiganov is known as a Liouville integrable Hamiltonian system with three degrees of freedom. For this system, we find some special periodic motions at which the momentum mapping has rank 1. For such motions, all phase variables can be expressed in terms of algeb...

In this paper we consider an integrable Hamiltonian system on the Lie algebra so(4) with an additional integral of the fourth degree - the Adler-van Moerbeke integrable case. We discuss classical works which explore, on the one hand, the dynamics of a rigid body with cavities completely filled with an ideal fluid performing a homogeneous vortex mot...

The Adler–van Moerbeke integrable case of the Euler equations on the Lie algebra so(4) is investigated. For the L–A pair found by Reyman and Semenov-Tian-Shansky for this system, we explicitly present a spectral curve and construct the corresponding discriminant set. The singularities of the Adler–van Moerbeke integrable case and its bifurcation di...

We consider a system consisting of a heavy circular cylinder in the field of gravity interacting dynamically with a vortex pair in a perfect fluid. The circulation about the cylinder is assumed to be zero. It is shown that, unlike the famous Föppl configuration, the vortices cannot be in a relative equilibrium. An asymptotic system and a suitable r...

В докладе рассматривается вполне интегрируемая гамильтонова система с двумя степенями свободы, которая описывает динамику волчка Ковалевской-Чаплыгина-Горячева-Яхья. Исходя из особенностей спектральной кривой, предъявлены разделенные уравнения Абеля--Якоби для некоторых значений параметров на нулевом уровне интеграла площадей. Впервые получен много...

В работе рассматривается интегрируемая гамильтонова система, описывающая движение в идеальной жидкости кругового цилиндра и вихревой нити. Построены бифуркационные диаграммы и бифуркационные комплексы в случае компактности интегрального многообразия и различной топологии симплектического листа. Обсуждаются типы движений, соответствующих бифуркацион...

We consider an integrable Hamiltonian system describing the motion of a circular cylinder and a vortex filament in an ideal fluid. We construct bifurcation diagrams and bifurcation complexes for the case in which the integral manifold is compact and for various topological structures of the symplectic leaf. The types of motions corresponding to the...

The case of motion of a generalized two-field gyrostat found by V.V.Sokolov and A.V.Tsiganov is known as a Liouville integrable Hamiltonian system with three degrees of freedom. We find a set of points at which the momentum map has rank 1. This set consists of special periodic motions which correspond to the singular points of a bifurcation diagram...

The case of motion of a generalized two-field gyrostat found by V.V.Sokolov and A.V.Tsiganov is known as a Liouville integrable Hamiltonian system with three degrees of freedom. We find a set of points at which the momentum map has rank 1. This set consists of special periodic motions which correspond to the singular points of a bifurcation diagram...

We consider a system that consists of a circular cylinder subject to gravity interacting with a point vortex in a perfect fluid. The circulation about the cylinder is equal to zero. The governing equations are Hamiltonian and admit the integral of motion (the horizontal component of the momentum). With the help of the autonomous integral, we reduce...

The problem of falling motion of a body in fluid has a long history and was considered in a series of the classical and modern papers. Some of the effects described in the papers, such as periodic rotation (tumbling), can be encountered only in viscous fluids and thus demand for their proper treatment the use of the Navier – Stokes equations with b...

The problem of falling motion of a body in fluid has a long history and was considered in a series of the classical and modern papers. Some of the effects described in the papers, such as periodic rotation (tumbling), can be encountered only in viscous fluids and thus demand for their proper treatment the use of the Navier – Stokes equations with b...

We consider a system which consists of a circular cylinder subject to gravity interacting with $N$ vortices in a perfect fluid. Generically, the circulation about the cylinder is different from zero. The governing equations are Hamiltonian and admit evident integrals of motion: the horizontal and vertical components of the momentum; the latter is...

The dynamical behavior of a heavy circular cylinder and N point vortices in an unbounded volume of ideal liquid is considered. The liquid is assumed to be irrotational and at rest at infinity. The circulation about the cylinder is different from zero. The governing equations are presented in Hamiltonian form. Integrals of motion are found. Allowabl...

The dynamical behavior of a heavy circular cylinder and a point vortex in an unbounded volume of ideal liquid is considered. The liquid is assumed to be irrotational and at rest at infinity. The circulation about the cylinder is different from zero. The governing equations are Hamiltonian and admit an evident autonomous integral of motion — the hor...

We consider a system which consists of a heavy circular cylinder and a point vortex in an unbounded volume of ideal liquid. The liquid is assumed to be irrotational and at rest at infinity. The circulation about the cylinder is different from zero. The equations governing the motion of a body interacting dynamically with point vortices were origin...

New analytical characteristics are proposed to describe the performance of an ion mobility increment spectrometer (IMIS). The dispersion describes the ability of such a spectrometer to separate ions with close values of the variable component of mobility. The necessary resolution limit with respect to this component characterizes the ability to sep...

A new method for determination of the non-constant component, alpha(E), of an ion mobility, k(E), is suggested. The method uses the relationship U(C) (US) that can be experimentally obtained with a spectrometer of ion mobility increment with planar drift chamber. (UC is a compensating voltage, U(S) is separating voltage amplitude.) A general equati...

A model for the drift of ions under a non-uniform, high-frequency electric field in the drift chamber of a spectrometer of ion mobility increment is developed. For the general dependence of the ion mobility on the electric field strength and the general time-dependence of the separating voltage, we suggest a procedure for calculating of the ion pea...

A model of nonlinear ion drift spectrometry for modern gas analyzers with separating chamber of cylindrical geometry is developed. In this case, a peak in the ionogram corresponds to the appearance of a limit cycle in the space of trajectories of the dynamical system. The experimentally observed ion beam focusing is theoretically calculated. For th...

The kinetic equation for the electron distribution function in a one-dimensional semiconductor with a spatial-periodic potential in the presence of a weak pulling electric field was analytically solved in the limiting case of the infinite length of carrier energy relaxation. An explicit expression for the conductivity of the system was derived for...

A consistent analytical model of nonlinear ion drift spectrometry for modern gas analyzers is developed. A procedure for determining the field dependence of the ion mobility using the experimental data is described. An ionogram is calculated for the case of a flat drift chamber and polynomial character of the field dependence of the ion mobility.