Математика список научных статей
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A Note on Forced Oscillations in Systems on a Plane
A sufficient condition for the existence of forced oscillations in nonautonomous systems on a plane is presented under the assumption that the magnitude of the nonautonomous perturbation is small. An advantage of the results presented over analytic methods is that they can be applied in degenerate...
2023 / I.Yu. PolekhinScopusВАКRSCIMathSciNetzbMATH -
On Nonlinear Oscillations of a Near-Autonomous Hamiltonian System in One Case of Integer Nonequal Frequencies
This paper is concerned with the motions of a near-autonomous two-degree-of-freedom Hamiltonian system, 2π-periodic in time, in a neighborhood of a trivial equilibrium. It is assumed that in the autonomous case, in the region where only necessary (which are not sufficient) conditions for the...
2023 / O. V. KholostovaScopusВАКRSCIMathSciNetzbMATH -
Complete Description of Bounded Solutions for a Duffing-Type Equation with a Periodic Piecewise Constant Coefficient
We consider the equation uxx − u + W(x)u3 = 0 where W(x) is a periodic alternating piecewise constant function. It is proved that under certain conditions for W(x) solutions of this equation, which are bounded on R, |u(x)| < ξ, can be put in one-to-one correspondence with bi-infinite sequences of...
2023 / G. L. Alfimov, M. E. LebedevScopusВАКRSCIMathSciNetzbMATH -
The Problem of the Rolling Motion of a Dynamically Symmetric Spherical Top with One Nonholonomic Constraint
This paper investigates the problem of a sphere with axisymmetric mass distribution rolling on a horizontal plane. It is assumed that the sphere can slip in the direction of the projection of the symmetry axis onto the supporting plane. Equations of motion are obtained and their first integrals are ...
2023 / A.A. Kilin, T.B. IvanovaScopusВАКRSCIMathSciNetzbMATH -
Nonlinear Orbital Stability of Periodic Motions in the Planar Restricted Four-Body Problem
We consider the planar circular restricted four-body problem with a small body of negligible mass moving in the Newtonian gravitational field of three primary bodies, which form a stable Lagrangian triangle. The small body moves in the same plane with the primaries. We assume that two of the...
2023 / B. S. Bardin, E.A. Sukhov, E.V. VolkovScopusВАКRSCIMathSciNetzbMATH -
Abnormal Extremals in the Sub-Riemannian Problem with Growth Vector (2, 3, 5, 8, 14)
We study the left-invariant sub-Riemannian problem on the free nilpotent Lie group of rank 2 and step 5. We describe some abnormal trajectories and some properties of the set filled by nice abnormal trajectories starting at the identity of the group.
2023 / Yu. L. Sachkov, E. F. SachkovaScopusВАКRSCIMathSciNetzbMATH -
A Study of a Mathematical Model with a Movable Singular Point in a Fourth-Order Nonlinear Differential Equation
This article introduces a mathematical model that utilizes a nonlinear differential equation to study a range of phenomena such as nonlinear wave processes, and beam deflections. Solving this equation is challenging due to the presence of moving singular points. The article addresses two main...
2023 / M. V. Gasanov, A. G. GulkanovScopusВАКRSCIMathSciNetzbMATH -
Analytical Solution of the Rayleigh – Plesset Equation Filled with Van Der Waals Gas for Various Isoprocesses
In this paper, we consider a mathematical model of the dynamics of the behavior of a spherically symmetric Rayleigh – Plesset bubble in the van der Waals gas model. The analysis of the model takes into account various isoprocesses without the presence of condensation and a model that takes into...
2024 / M. V. Gasanov, A. G. Gulkanov, K.A. ModestovScopusВАКRSCIMathSciNetzbMATH -
Analysis of the Force and Torque Arising During the Oscillatory Motion of a Joukowsky Foil in a Fluid
The problem of describing the motion of a rigid body in a fluid is addressed by considering a symmetric Joukowsky foil. Within the framework of the model of an ideal fluid, the force and torque acting on an unsteady moving foil are calculated. The analytical results are compared with those obtained ...
2024 / E.V. Vetchanin, A.R. ValievaScopusВАКRSCIMathSciNetzbMATH -
On the Orbital Stability of Periodic Motions of a Heavy Rigid Body in the Bobylev – Steklov Case
The problem of the orbital stability of periodic motions of a heavy rigid body with a fixed point is investigated. The periodic motions are described by a particular solution obtained by D. N. Bobylev and V. A. Steklov and lie on the zero level set of the area integral. The problem of nonlinear...
2024 / Boris S. BardinScopusВАКRSCIMathSciNetzbMATH -
On the Dynamics of a Biped upon a Moving Rough Plane
We consider the planar problem of the dynamics of a body moving along a horizontal with two legs in contact with a rough horizontal plane. Possible types of movements of the body are discussed depending on the acceleration of the support: relative equilibrium, sliding on two legs, lifting off one...
2024 / Alexander P. IvanovScopusВАКRSCIMathSciNetzbMATH -
On Two-Dimensional Diffeomorphisms with Homoclinic Orbits to Nonhyperbolic Fixed Points
We consider two-dimensional diffeomorphisms with homoclinic orbits to nonhyperbolic fixed points. We assume that the point has arbitrary finite order degeneracy and is either of saddlenode or weak saddle type. We consider two cases when the homoclinic orbit is transversal and when a quadratic...
2024 / Sergey V. Gonchenko, Olga V. GordeevaScopusВАКRSCIMathSciNetzbMATH -
Morse – Smale 3-Diffeomorphisms with Saddles of the Same Unstable Manifold Dimension
In this paper, we consider a class of Morse – Smale diffeomorphisms defined on a closed 3-manifold (not necessarily orientable) under the assumption that all their saddle points have the same dimension of the unstable manifolds. The simplest example of such diffeomorphisms is the well-known...
2024 / Eugene M. Osenkov, O.V. PochinkaScopusВАКRSCIMathSciNetzbMATH -
Description of Trajectories of an Evolution Operator Generated by Mosquito Population
In this paper, we study discrete-time dynamical systems generated by the evolution operator of mosquito population. An invariant set is found and a Lyapunov function with respect to the operator is constructed in this set. Using the Lyapunov function, the global attraction of a fixed point is...
2024 / Zafar S. BoxonovScopusВАКRSCIMathSciNetzbMATH -
On a Method for Integrating the Equations of Rigid Body Motion in Three Homogeneous Force Fields
This paper presents a method for integrating the equations of motion of a rigid body having a fixed point in three homogeneous force fields. It is assumed that under certain conditions these equations admit an invariant relation that is characterized by the following property: the velocity of...
2024 / Gennadii V. GorrScopusВАКRSCIMathSciNetzbMATH -
Physically Admissible and Inadmissible Exact Localized Solutions in Problems of Nonlinear Wave Dynamics of Cylindrical Shells
It is shown that, when studying nonlinear longitudinal deformation waves in cylindrical shells, it is possible to obtain physically admissible solitary wave solutions using refined shell models. In the article, a physically admissible exact localized solution based on the Flügge – Lurie – Byrne...
2024 / Aleksandr I. Zemlyanukhin, A.V. Bochkarev, N.A. ArtamonovScopusВАКRSCIMathSciNetzbMATH -
On the Phenomenon of Low-Frequency, Large-Amplitude Oscillations in a High-Dimensional Linear Dynamical System
This article considers a linear dynamic system that models a chain of coupled harmonic oscillators, under special boundary conditions that ensure a balanced energy flow from one end of the chain to the other. The energy conductivity of the chain is controlled by the parameter α of the system. In a...
2024 / Aleksey I. Gudimenko, Andrey V. LihosherstovScopusВАКRSCIMathSciNetzbMATH -
VERSIONS OF THE “ONION HUSK” ALGORITHM IN THE PSEUDO-GEOMETRIC TRAVELING SALESMAN PROBLEM WITH A SMALL VARIANCE
We continue to consider the pseudo-geometric traveling salesman problem. Specifically, we are considering several auxiliary algorithms needed to implement different versions of the “onion husk” algorithm. We have not found in the literature an accurate description of specific versions of algorithms ...
2023 / Boris Melnikov, Elena MelnikovaВАК -
О ВТОРОЙ ТЕОРЕМЕ АБЕЛЯ
Даётся небольшой обзор существующих доказательств второй теоремы Абеля и приводится более простой вариант доказательства этой фундаментальной теоремы.
2024 / Е. В. МельниковВАК -
Графическая программа перехода геологических нарушений механизированными комплексами
Ведение очистных работ в зонах геологических нарушений связано с необходимостью маневрирования комплексом в вертикальной плоскости и осложняется присечением боковых пород и вывалообразованием в кровле. В нормативных документах траектория перехода рассматривается только в разрезе по простиранию...
2024 / Мирошников Г.П., Самойленко Л.В.ScopusВАКCASGeoRef