Maxim V. Shamolin

Maxim V. Shamolin
Lomonosov Moscow State University | MSU · Institute of Mechanics

Doctor of Sciences (Physical an Mathematical)
Expert of Russian Academy of Sciences

About

582
Publications
19,472
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
2,640
Citations
Introduction
The research presents the review of cases of integrability obtained earlier and also new in two-, three-, and four-dimensional rigid body dynamics in a nonconservative force field. The problems studied are described in terms of so-called zero mean variable dissipation dynamical systems. Therefore, we study nonconservative systems for which the usual methods, for example, Hamiltonian systems, are not applicable in general.
Additional affiliations
August 2005 - present
Lomonosov Moscow State University
Position
  • Professor (Full)
October 1992 - present
Lomonosov Moscow State University
Position
  • Leading Scientist, (Full) Professor
Education
September 1983 - June 1988
Lomonosov Moscow State University
Field of study
  • Theoretical Mechanics

Publications

Publications (582)
Article
Full-text available
Digital technologies are known to have high potential for economic growth and to promote social and political communications. They are platforms for implementing new business ideas. A new digital phenomenon— information business, or infobusiness—is investigated in the article. How does information business affect the economy and society? This quest...
Article
Tensor invariants (first integrals and differential forms) of homogeneous dynamical systems on tangent bundles to smooth three-dimensional manifolds (systems with three degrees of freedom) are presented in this paper. The connection between the presence of such invariants and the complete set of the first integrals, which are necessary for the inte...
Article
Full-text available
Digital technologies are known to have high potential for economic growth, to promote social and political communications. They are platforms for the implementation of new business ideas. New digital phenomenon ”— the information business ”— is investigated in the article. How does information business affect the economy and society? This question...
Article
Full-text available
In this activity, we systematize some results on the study of the equations of a motion of dynamically symmetric four-dimensional fixed rigid bodies-pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study th...
Article
Full-text available
New cases of integrable dynamical systems of the ninth order homogeneous in terms of variables are presented, in which a system on a tangent bundle to a four-dimensional manifold can be distinguished. In this case, the force field is divided into an internal (conservative) and an external one, which has a dissipation of a different sign. The extern...
Article
We study the non-conservative systems for which the methods for studying, for example, Hamiltonian systems is not applicable in general. Therefore, for such systems, it is necessary, in some sense, to “directly” integrate the main equation of dynamics. Herewith, we offer more universal interpretation of both obtained cases and new ones of complete...
Article
Full-text available
New cases of integrable dynamical systems of the seventh order homogeneous in terms of variables are presented, in which a system on a tangent bundle to a three-dimensional manifold can be distinguished. In this case, the force field is divided into an internal (conservative) and an external one, which has a dissipation of a different sign. The ext...
Article
New cases of integrable dynamical systems of the ninth order homogeneous in terms of variables are presented, in which a system on a tangent bundle to a four-dimensional manifold can be distinguished. In this case, the force field is divided into an internal (conservative) and an external one, which has a dissipation of a different sign. The extern...
Article
Full-text available
Tensor invariants (differential forms) for homogeneous dynamical systems on tangent bundles to smooth two-dimensional manifolds are presented in the paper. The connection between the presence of these invariants and the full set of first integrals necessary for integration of geodesic, potential, and dissipative systems is shown. At the same time,...
Article
Full-text available
Tensor invariants (first integrals and differential forms) of homogeneous dynamical systems on the tangent bundles of smooth three-dimensional manifolds (systems with three degrees of freedom) are presented in this paper. The connection between the presence of such invariants and the complete set of the first integrals needed for the integration of...
Article
В работе предъявлены тензорные инварианты (первые интегралы и дифференциальные формы) для однородных динамических систем на касательных расслоениях к гладким двумерным многообразиям. Показана связь наличия данных инвариантов и полного набора первых интегралов, необходимых для интегрирования геодезических, потенциальных и диссипативных систем. При э...
Article
New cases of integrable seventh-order dynamical systems that are homogeneous with respect to some of the variables are presented, in which a system on the tangent bundle of a three-dimensional manifold can be distinguished. In this case, the force field is divided into an internal (conservative) and an external component, which has dissipation of d...
Article
New cases of integrable fifth-order dynamical systems that are homogeneous with respect to some of the variables are obtained, in which a system on the tangent bundle of a two-dimensional manifold can be distinguished. In this case, the force field is divided into an internal (conservative) and an external one, which has dissipation of different si...
Article
Full-text available
The implementation of «The Scientific and Technological Development Strategy of the Russian Federation» and national projects is impossible without an inflow of new entrepreneurs. Young people including students are most active in business creation among the entire Russian people. The object of this study is students’ entrepreneurial intentions, an...
Article
It is well known that a system of differential equations can be exactly integrated if a sufficient number of its tensor invariants (not only first integrals) are found. For example, if there is an invariant differential form of the phase volume, the number of required first integrals can be reduced. For conservative systems, this fact is natural, b...
Article
New cases of integrable dynamical systems of the fifth order homogeneous in terms of variables are obtained, in which a system on a tangent bundle to a two-dimensional manifold can be distinguished. In this case, the force field is divided into an internal (conservative) and an external one, which has a dissipation of a different sign. The external...
Article
As is well-known [1–3], finding a sufficient number of tensor invariants (not only the first integrals) allows you to accurately integrate a system of differential equations. For example, the presence of an invariant differential form of the phase volume makes it possible to reduce the number of required first integrals. For conservative systems, t...
Article
Complete sets of invariant differential forms of phase volume for homogeneous dynamical systems on tangent bundles of smooth four-dimensional manifolds are presented. The connection between the existence of these invariants and the complete set of first integrals necessary for the integration of geodesic, potential, and dissipative systems is shown...
Chapter
Tensor invariants (differential forms) for homogeneous dynamical systems on tangent bundles to smooth two-dimensional manifolds are presented in this paper. The connection between the presence of these invariants and the full set of the first integrals necessary for the integration of geodesic, potential and dissipative systems is shown. At the sam...
Article
Full-text available
In this paper, we prove the integrability of some classes of odd-order dynamical systems (namely, systems of order 3, 5, and 7), which are homogeneous in some variables and contain a system on the tangent bundle of a smooth manifolds. In this case, we separate force fields into internal (conservative) and external, which has sign-alternating dissip...
Article
Full-text available
In the paper, combinatorial theorems related to the theory of social choice are obtained. These theorems describe general conditions under which the problem on the preserving the preference set 𝒟 by an arbitrary aggregation rule f and the problem on the compatibility of the preference set 𝒟 with a pair (f, 𝒞) can be reduced to similar problems for...
Article
Full-text available
This paper is devoted to the study of the relative structural stability (the relative roughness) of dynamical systems considered not on the whole space of dynamical systems, but only on a certain subspace of it. Moreover, the space of deformations of dynamical systems also does not coincide with the whole space of admissible deformations. In partic...
Article
Full-text available
We consider a mathematical model of the plane-parallel action of a medium on a rigid body whose surface contains a cone-shaped being part. A complete system of equations of motion under in the quasi-stationary case is presented. A new family of phase portraits on the phase cylinder of quasi-velocity is obtained. Also, we consider a mathematical mod...
Article
Tensor invariants (differential forms) for homogeneous dynamical systems on tangent bundles of smooth three-dimensional manifolds are presented. The connection between the presence of these invariants and the full set of first integrals necessary for the integration of geodesic, potential, and dissipative systems is shown. The introduced force fiel...
Article
Complete set of invariant differential forms of phase volume for homogeneous dynamical systems on tangent bundles to smooth four-dimensional manifolds are presented in this paper. The connection between the presence of these invariants and the complete set of the first integrals which are necessary for the integration of geodesic, potential and dis...
Article
Full-text available
This work is the eighth work of the cycle on differential and topological diagnostics. In it, a qualitative and numerical mathematical experiment is carried out to diagnose the control system of an aircraft during its planning from altitudes close to orbital, with an initial velocity close to the first cosmic velocity. And we have shown that the pr...
Article
Full-text available
Proposed work is the seventh work of the cycle on differential and topological diagnostics. Diagnostics ofmalfunctions in the system of indirect control of an object whose motion is described by nonlinear ordinary differential equations of the third order (the problem of B.V. Bulgakov) is considered. In the diagnostic algorithm used, the scope of c...
Article
Full-text available
Study of the dynamics of a multidimensional solid depends on the force-field structure. As reference results, we consider the equations of motion of low-dimensional solids in the field of a medium-drag force. Then it becomes possible to generalize the dynamic part of equations to the case of the motion of a solid, which is multidimensional in a sim...
Article
Full-text available
It is well known that a system of differential equations can be exactly integrated if a sufficient number of its tensor invariants (not only first integrals) are found. For example, if there is an invariant differential form of the phase volume, the number of required first integrals can be reduced. For conservative systems, this fact is natural, b...
Article
Full-text available
This paper is the first part of a survey on the integrability of systems with a large number n of degrees of freedom. The review consists of three parts. In this first part, the primordial problem from the dynamics of a multidimensional rigid body placed in a nonconservative force field is described in detail. In the second and third parts, which w...
Article
Full-text available
Proposed work is the sixth work of the cycle on differential and topological diagnostics. It is shown that the diagnostics in the case of trajectorial measurements corrupted by noise, which is a stochastic process of the normal white noise type with zero mean value and bounded spectrum, can be performed by using the diagnostic algorithms obtained i...
Article
Tensor invariants (differential forms) for homogeneous dynamical systems on tangent bundles of smooth two-dimensional manifolds are presented. The connection between the presence of these invariants and the full set of first integrals necessary for the integration of geodesic, potential, and dissipative systems is shown. The force fields introduced...
Article
Full-text available
We systematize some results on the study of the equations of spatial motion of dynamically symmetric fixed rigid bodies–pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of a spatial motion...
Article
Full-text available
Proposed activity presents next stage of the study of the problem of the plane-parallel motion of a rigid body interacting with a resistant medium through the frontal plane part of its external surface. Under constructing of the force acting of medium, we use the information on the properties of medium streamline fl w around in quasistationarity co...
Article
Full-text available
This paper is devoted to the study of the motion of a platform maintained on an aircraft in a predetermined position by a system of gyroscopes, which does follows oscillations of the aircraft. Such systems are used for determining the angular position of the aircraft. We briefly review key results on this issue without detailed proofs.
Article
Full-text available
The presented work is devoted to the problem of motion in a resisting medium of a rigid body whose surface of contact with the medium is only a plane part of its exterior surface. In this case, the force field is constructed from the reasons for the medium action on the body under the streamline (or separation) flow around and quasi‐stationarity co...
Article
Full-text available
Proposed work is the fourth in the cycle, therefore, the diagnostic problem is formulated for the case ofexact trajectorial measurements, the diagnostic theorem is stated and proved, and two diagnostic algorithmsthat follow from this theorem are presented. Techniques for an a priori counting of constants, which shouldbe stored in a program for the...
Article
Full-text available
The so-called pendulum-like systems arise in dynamics of a rigid body in a nonconservative field, in the theory of oscillations, and in theoretical physics. In this article, the methods of analysis are described which allow us to generalize the previous results. Herewith, we deal with some qualitative questions of the theory of ordinary differentia...
Article
Full-text available
We establish the integrability of homogeneous (in some variables) dynamical systems with dissipation in the case of an arbitrary odd order and thereby generalize the results earlier obtained by the author in particular cases of such systems.
Article
Full-text available
При изучении случаев интегрируемости многомерного твердого тела в неконсервативных силовых полях автором реализуются два подхода. Первый подход касается систем, в которых неконсервативность силового поля порождается введением дополнительных коэффициентов в кинематические соотношения; особняком здесь стоят случаи $n=5$ и $n=6$. Второй же подход осно...
Article
В данной работе затрагиваются некоторые качественные вопросы теории обыкновенных дифференциальных уравнений, от решения которых зависит исследование ряда динамических систем. Элементарному обзору подлежат такие проблемы как качественные вопросы теории топографических систем Пуанкаре и более общих систем сравнения; проблемы существования и единствен...
Article
Предложена методика исследования систем возле сингулярных особых точек, т.е. точек, в окрестности которых невозможно разложить в ряд векторное поле системы. Применяются методы теории многомерных топографических систем Пуанкаре для поиска притягивающих режимов в системе.
Article
В работе показана интегрируемость некоторых классов однородных по части переменных динамических систем девятого порядка, в которых выделяется система на касательном расслоении к четырехмерным многообразиям. При этом силовые поля обладают диссипацией разного знака и обобщают ранее рассмотренные.
Article
Full-text available
In this paper, we prove the integrability of certain classes of dynamical systems on the tangent bundles of four-dimensional manifolds (systems with four degrees of freedom). The force field considered possessed so-called variable dissipation; they are generalizations of fields studied earlier. This paper continues earlier works of the author devot...
Article
Full-text available
In this paper, we examine the problem on the spatial free deceleration of a rigid body in a resistive medium under the assumption that the interaction of the homogeneous axisymmetric body with the medium is concentrated on the frontal part of the surface, which has the shape of a flat circular disk. In earlier works of the author, under the simples...
Article
Full-text available
In this paper, we prove the integrability of certain classes of dynamical systems on the tangent bundles of three-dimensional manifolds (systems with three degrees of freedom). The force field considered possesses so-called variable dissipation; they are generalizations of fields studied earlier.
Article
Full-text available
We consider the problem of differential diagnostics of the functional status of control objects that have a module structure and a finite set of possible malfunctions and reduce this problem to two separate problems that can be solved separately: the inspection problem (ascertainment of malfunction criteria in the system) and the diagnostic problem...
Article
Full-text available
In this paper, we prove the integrability of certain classes of dynamical systems that appear in the dynamics of multidimensional rigid bodies and the dynamics of a particle moving on a multidimensional sphere. The force field considered has the so-called variable dissipation with zero mean; they are generalizations of fields studied earlier. We pr...
Article
Full-text available
The so-called pendulum-like systems arise in dynamics of a rigid body in a nonconservative field, in the theory of oscillations, and in theoretical physics. In this article, the methods of analysis are described which allow us to generalize the previous results. Herewith, we deal with some qualitative questions of the theory of ordinary differentia...
Article
The integrability of certain classes of homogeneous dynamical systems on the tangent bundles of three-dimensional manifolds is shown. The force fields involved in the systems lead to dissipation of variable sign and generalize previously considered fields.
Article
Full-text available
In this review, we discuss new cases of integrable systems on the tangent bundles of finite-dimensional spheres. Such systems appear in the dynamics of multidimensional rigid bodies in nonconservative fields. These problems are described by systems with variable dissipation with zero mean. We found several new cases of integrability of equations of...
Article
The integrability of certain classes of homogeneous dynamical systems on the tangent bundles of two-dimensional manifolds is shown. The force fields involved in the systems lead to dissipation of variable sign and generalize previously considered fields.
Chapter
In this work, the integrability of some classes of dynamic systems on tangent bundles of three-dimensional manifolds is demonstrated. The corresponding force fields possess the so-called variable dissipation and generalize those considered earlier.
Article
Full-text available
Proposed work is the fifth work of the cycle on differential and topological diagnostics. The article gives an estimate of the errors method of direction fields in the case of not accurate trajectory measurements, but trajectory measurements with an error are limited by the modulus of a given a smooth function of time, and in case this error is a r...
Article
Full-text available
In this paper, we prove the explicit integrability of certain classes of dynamical systems on the tangent bundles of 2- and 3-dimensional spheres in the case where the forces are fields with so-called variable dissipation.
Article
The description of dissipation in a dynamical system is a difficult problem. For example, this can be done as follows: certain coefficients indicate that energy is scattered in some domains of the phase space and is pumped into other domains. This leads to the loss of classical first integrals (conservation laws), which are globally expressed in te...
Article
Full-text available
In many problems of dynamics, one has to deal with mechanical systems whose configurational spaces are two- or three-dimensional manifolds. For such a system, the phase space naturally coincides with the tangent bundle of the corresponding manifold. Thus, the problem of a flow past a (four-dimensional) pendulum on a (generalized) spherical hinge le...
Article
Full-text available
We consider consecutive aggregation procedures for individual preferences 𝔠 ∈ ℭr (A) on a set of alternatives A, |A| ≥ 3: on each step, the participants are subject to intermediate collective decisions on some subsets B of the set A and transform their a priori preferences according to an adaptation function 𝒜. The sequence of intermediate decision...
Article
Full-text available
We establish the integrability for a class of homogeneous (with respect to a part of variables) dynamic systems of odd (seventh and ninth) order, admitting separation of a system on the tangent bundle of smooth manifolds. Bibliography: 13 titles.
Article
Full-text available
В работе показана интегрируемость некоторых классов однородных по части переменных динамических систем нечетного (третьего, пятого и седьмого) порядка, в которых выделяется система на касательном расслоении к гладким многообразиям. При этом силовое поле разделяется на внутреннее (консервативное) и внешнее, которое обладает диссипацией разного знака...
Article
Работа посвящена исследованию вопросов относительной структурной устойчивости (относительной грубости) динамических систем, рассматриваемых не на всем пространстве динамических систем, а лишь на некотором его подпространстве. При этом пространство деформаций динамических систем также не совпадает со всем пространством допустимых деформаций. В частн...
Article
В работе получены комбинаторные теоремы, относящиеся к теории коллективного выбора. Эти теоремы описывают достаточно общие условия, при которых задача о сохранении произвольным правилом агрегирования $f$ множества предпочтений $\mathcal{D}$ и задача о совместимости множества предпочтений $\mathcal{D}$ с парой $(f,\mathcal{C})$ могут быть сведены к...
Article
Рассмотрена математическая модель плоскопараллельного воздействия среды на твердое тело, частью участка внешней поверхности которого является круговой конус. Приведена полная система уравнений движения в условиях квазистационарности. Получено новое семейство фазовых портретов на фазовом цилиндре квазискоростей. Также рассмотрена математическая моде...
Article
Full-text available
Proposed work is the third in the cycle, therefore, we explain such notions as checking sphere, checking ellipsoid and checking tubes. The checking problem is stated and the algorithms for solving it are formulated. The criterion for a malfunction in a controlled system whose motion is described by ordinary differential equations is taken to be the...
Article
Full-text available
The paper shows the integrability of certain classes of ninth-order dynamic systems that are homogeneous in part, in which the system on the tangent bundle to four-dimensional manifolds is distinguished. In this case, the force fields have various dissipation and generalize the previously considered ones.
Article
Integrability is shown for certain classes of ninth-order dynamic systems homogeneous on the part of variables in which a system on the tangent bundle to the four-dimensional manifolds is singled out. In this case, the force fields have dissipation of different signs and generalize the situations considered previously.
Article
The integrability of certain classes of dynamical systems on the tangent bundle of a multidimensional manifold is shown. In this case, the force fields with variable dissipation generalize those considered earlier.
Article
Full-text available
Proposed work is the second in the cycle, therefore, we present the classification of malfunctions and introduce the concept of reference malfunctions that can occur in the control system of the object and in the neighborhoods of these malfunctions. The simplest possible approaches to mathematical modeling of malfunctions and their neighborhoods ar...

Questions

Questions (3)
Question
What is the ratio of full energy and kinetic moment?
Question
What is the sample of the four-dimensional rigid body in our real life?
Question
In mathematics and theoretical physics What are the cases of integrability in elementary functions of the dissipative systems do you know?
See my articles. Maxim V. Shamolin

Network

Cited By