Математика список научных статей
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On the Orbital Stability of Pendulum Oscillations of a Dynamically Symmetric Satellite
The orbital stability of planar pendulum-like oscillations of a satellite about its center of mass is investigated. The satellite is supposed to be a dynamically symmetrical rigid body whose center of mass moves in a circular orbit. Using the recently developed approach [1], local variables are...
2022 / B. S. Bardin, E.A. Chekina, A.M. ChekinScopusВАКRSCIMathSciNetzbMATH
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Gyrostatic Suslov Problem
In this paper, we investigate the gyrostat under influence of an external potential force with the Suslov nonholonomic constraint: the projection of the total angular velocity onto a vector fixed in the body vanishes. We investigate cases of free gyrostat, the heavy gyrostat in the constant gravity ...
2022 / A. J. Maciejewski, M. PrzybylskaScopusВАКRSCIMathSciNetzbMATH -
Nonintegrability of the Problem of the Motion of an Ellipsoidal Body with a Fixed Point in a Flow of Particles
The problem of the motion, in the free molecular flow of particles, of a rigid body with a fixed point bounded by the surface of an ellipsoid of revolution is considered. This problem is similar in many aspects to the classical problem of the motion of a heavy rigid body about a fixed point. In...
2022 / M. M. Gadzhiev, A. S. KuleshovScopusВАКRSCIMathSciNetzbMATH -
Spacecraft with Periodic Mass Redistribution: Regular and Chaotic Behaviour
The motion of a spacecraft containing a moving massive point in the central field of Newtonian attraction is considered. Within the framework of the so-called “satellite approximation”, the center of mass of the system is assumed to move in an unperturbed elliptical Keplerian orbit. The...
2022 / A. A. Burov, I. I. Kosenko, V. I. NikonovScopusВАКRSCIMathSciNetzbMATH -
Formal Asymptotics of Parametric Subresonance
The article is devoted to a comprehensive study of linear equations of the second order with an almost periodic coefficient. Using an asymptotic approach, the system of equations for parametric subresonant growth of the amplitude of oscillations is obtained. Moreover, the time of a turning point...
2022 / P. Astafyeva, O. KiselevScopusВАКRSCIMathSciNetzbMATH -
The Integrable Problem of the Rolling Motion of a Dynamically Symmetric Spherical Top with One Nonholonomic Constraint
This paper addresses the problem of a sphere with axisymmetric mass distribution rolling on a horizontal plane. It is assumed that there is no slipping of the sphere as it rolls in the direction of the projection of the symmetry axis onto the supporting plane. It is also assumed that, in the...
2023 / A.A. Kilin, T.B. IvanovaScopusВАКRSCIMathSciNetzbMATH -
On a Classification of Periodic Maps on the 2-Torus
In this paper, following J. Nielsen, we introduce a complete characteristic of orientationpreserving periodic maps on the two-dimensional torus. All admissible complete characteristics were found and realized. In particular, each of the classes of orientation-preserving periodic homeomorphisms on...
2023 / D.A. Baranov, V. Z. Grines, O.V. Pochinka, E. E. ChilinaScopusВАКRSCIMathSciNetzbMATH -
Oscillations in Dynamic Systems with an Entropy Operator
This paper considers dynamic systems with an entropy operator described by a perturbed constrained optimization problem. Oscillatory processes are studied for periodic systems with the following property: the entire system has the same period as the process generated by its linear part. Existence...
2023 / Y. S. PopkovScopusВАКRSCIMathSciNetzbMATH -
On a Classification of Chaotic Laminations which are Nontrivial Basic Sets of Axiom A Flows
We prove that, given any n > 3 and 2 < q < n−1, there is a closed n-manifold Mn admitting a chaotic lamination of codimension q whose support has the topological dimension n − q + 1. For n = 3 and q = 2, such chaotic laminations can be represented as nontrivial 2-dimensional basic sets of axiom A...
2023 / V. S. Medvedev, E.V. ZhuzhomaScopusВАКRSCIMathSciNetzbMATH -
A Remark on Tonelli’s Calculus of Variations
This paper provides a quite simple method of Tonelli’s calculus of variations with positive definite and superlinear Lagrangians. The result complements the classical literature of calculus of variations before Tonelli’s modern approach. Inspired by Euler’s spirit, the proposed method employs...
2023 / Kohei SogaScopusВАКRSCIMathSciNetzbMATH -
On a Class of Precessions of a Rigid Body with a Fixed Point under the Action of Forces of Three Homogeneous Force Fields
This paper is concerned with a special class of precessions of a rigid body having a fixed point in a force field which is a superposition of three homogeneous force fields. It is assumed that the velocity of proper rotation of the body is twice as large as its velocity of precession. The...
2023 / G. V. GorrScopusВАКRSCIMathSciNetzbMATH -
Evolutionary Behavior in a Two-Locus System
In this short note we study a dynamical system generated by a two-parametric quadratic operator mapping a 3-dimensional simplex to itself. This is an evolution operator of the frequencies of gametes in a two-locus system. We find the set of all (a continuum set of) fixed points and show that each...
2023 / A.M. Diyorov, U. A. RozikovScopusВАКRSCIMathSciNetzbMATH -
Topology of Ambient 3-Manifolds of Non-Singular Flows with Twisted Saddle Orbit
In the present paper, nonsingular Morse – Smale flows on closed orientable 3-manifolds are considered under the assumption that among the periodic orbits of the flow there is only one saddle and that it is twisted. An exhaustive description of the topology of such manifolds is obtained. Namely, it...
2023 / O.V. Pochinka, D.D. ShubinScopusВАКRSCIMathSciNetzbMATH -
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
