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Departments

Applied Mechanics Department

Research

Department history

Publications

P.V. Kharlamov biography

P.V. Kharlamov works

List of publications

Research Interests:

Analytic dynamics of a rigid body and rigid bodies systems
Application of topological methods to investigation of integrable and non-integrable Hamiltonian systems
Stability theory for invariant sets of nonlinear impulsive systems
Nonlinear control theory, inverse control systems
Methods of computer modeling and visualization in dynamics of a rigid body
Dynamics and stability of wheeled vehicles and gyroscopes suspended by gimbal

Selected Books:

1. Kharlamov P.V. Lectures on Dynamics of a Rigid Body. – Novosibirsk Univ., 1965. – 221 p.

2. Kharlamov P.V. General Mechanics. – Donetsk Univ., 1970. – 175 p.

3. Savchenko A.Ya. Stability of Stationary Motions of Mechanical Systems. – Kiev: Naukova Dumka, 1977. – 160 p.

4. Gorr G.V., Kudryashova L.V., Stepanova L.A.

Classical Problems in the Dynamics of Rigid Bodies. Their Development and Current State. – Kiev: Naukova Dumka, 1978. – 294 p.

5. Ilyukhin A.A. Three-dimensional Problems of the Nonlinear Theory of Elastic Rods. – Kiev: Naukova Dumka, 1979. – 216 p.

6. Kovalev A.M. Nonlinear Problems of Control and Observation in the Theory of Dynamical Systems. – Kiev: Naukova Dumka, 1980. – 175 p.

7. Gorr G.V., Ilyukhin A.A., Kovalev A.M., Savchenko A.Ya. Nonlinear Analysis of the Behavior of Mechanical Systems. – Kiev: Naukova Dumka, 1984. – 288 p.

8. Kharlamova E.I., Mozalevskaya G.V.

An Integro-Differential Equation for the Dynamics of a Rigid Body. – Kiev: Naukova Dumka, 1986. – 296 p.

9. Savchenko A.Ya., Ignatyev A.O. Some Problems in the Stability of Nonautonomous Dynamical Systems. – Kiev: Naukova Dumka, 1989. – 208 p.
10. Lobas L.G., Verbitskii V.G.

Qualitative and Analytical Methods in the Dynamics of Wheel Machines. – Kiev: Naukova Dumka, 1990. – 232 p.

11. Dokshevich A.I.

Closed-form Solutions of the Euler-Poisson Equations. – Kiev: Naukova Dumka,1992. – 168 p.

12. Kovalev A.M., Shcherbak V.F.

Controllability, Observability, Identifiablity of Dynamical Systems. – Kiev: Naukova Dumka, 1993. – 235 p.

13. Kharlamov P.V.

Essays on Foundations of Mechanics. – Kiev: Naukova Dumka, 1995. – 407 p.

14. Lesina M.E. On the Mathematical Model of a Gyro-Sphere. – Donetsk Tech. Univ, 1996. – 104 p.

15. Lesina M.E. Exact Solutions of the Two New Problems of Analytical Dynamics of Systems of Coupled Bodies. – Donetsk Tech. Univ., 1996. – 238 p.

16. Lesina M.E. The Problem on Motion of the System of Rigid Bodies. – Donetsk Tech. Univ., 1998. – 156 p.

17. Lesina M.E., Kudryashova L.V. New Formulation and Solution of Problems of the Dynamics of the System of Bodies. – Donetsk Tech. Univ., 1999. – 268 p.

18. Kharlamov P.V. Selected Works. – Kiev: Naukova Dumka, 2005. – 255 p.
19. Lesina M.E. Methods of Nonlinear Oscillations in the Problem of Motion of a System of Rigid Bodies. – Kiev: Naukova Dumka, 2005. – 194 p.

20. Verbitskii V.G., Danilenko E., Nowak A., Sitarz M. Introduction in the Stability Theory of the Wheel Vehicles and Railway. – «Veber» (Donetsk department), 2007. – 255 p.

21. Gorr G.V., Maznev A.V., Shchetinina E.K. Precessional Motions in Rigid Body Dynamics and in Dynamics of a System of Coupled Rigid Bodies. – Donetsk Nat. Univ., 2009. – 222 p.

22. Gorr G.V., Maznev A.V. Dynamics of a Gyrostat Having a Fixed Point. – Donetsk Nat. Univ., 2010. – 364 p.

23. Gashenenko I.N., Gorr G.V., Kovalev A.M. Classical Problems of the Rigid Body Dynamics. – Kiev: Naukova Dumka, 2012. – 402 p.

HEAD OF THE DEPARTMENT

During 1965-2001 Correspondent Member of the Ukrainian Academy of Sciences P.V. Kharlamov was the head of the department. In the period 2001-2009 the head of the department was doctor of physical and mathematical sciences, professor E.I. Kharlamova. Since 2009 the head of the department is doctor of physical and mathematical sciences I.N. Gashenenko.

STAFF OF THE DEPARTMENT

1. Leading research workers, doctors of physical and mathematical sciences, professors G.V. Gorr, A.O. Ignatyev, M.E. Lesina, V.G. Verbitskii.

2. Senior research workers: doctor of physical and mathematical sciences B.I. Konosevich, candidate of physical and mathematical sciences G.V. Mozalevskaya.

3. Research workers: candidates of physical and mathematical sciences Yu.B. Konosevich and O.S. Volkova.

4. Engineers D.N. Tkachenko, N.V. Voloshina.

HISTORIC INFORMATION

The department of applied mechanics was one among the first departments created in 1965 at Computer Center of AS Ukrainian SSR. In 1970 Computer Center was reorganized in the Institute of applied mathematics and mechanics (IAMM). Scientific and organizational work at the department was leaded by Correspondent Member of AS UkSSR P.V. Kharlamov, who had worked before that time in the Institute of Hydrodynamics of AS USSR and Novosibirsk State University.

Together with P.V. Kharlamov a few students of Novosibirsk State University G.V. Gorr, A.A. Iljukhin, B.I. Konosevich, A.M. Kovalev, Yu.M. Kovalev, E.V. Pozdnyakovich, A.Ya. Savchenko, research workers of Institute of Hydrodynamics of Siberian department of AS USSR G.V. Mozalevskaya, N.S. Khapilova came to Donetsk together with A.I. Dokshevich fr om the Institute of Mathematics of AS Uzbekistan SSR. During 40 years 8 doctoral and 40 candidate thesises were prepared and successfully defended by the scientific workers of the department. At different times among its scientific staff were A.M. Kovalev (from 1967 to 1996), A.Ya. Savchenko (from 1971 to 1978), A.I. Dokshevich (from 1966 to 1995), V.S. Elfimov (from 1975 to 1995), V.I. Koval (from 1971 to 1977), S.V. Kuznetsov (from 1966 to 1972), E.V. Pozdnyakovich (from 1969 to 1974), A.A. Iljukhin (from 1966 to 1979), N.V. Hlustunova (from 1997 to 2005), V.F. Shcherbak (from 1979 to 2012).

The research workers of the department are maintaining the close professional contacts with the former staff members of the department and post-graduate students of IAMM who are working now at the various educational institutions in the Donetsk region, in particular, Donetsk State University, Donetsk State Technical University, Donbass Regional Academy of Building and Architecture, Donetsk Institute of Artificial Intellect, Donetsk Institute of Railway Transport etc.

Beginning from 1969 the scientific journal "Mechanics of rigid bodies" is annually published at the department. The journal is included in the list of specialized editions of High Certifying Commission of Ukraine. During 1984-1991 the journal was translated into English by "Allerton Press" (New York, USA). Since 1984 the journal is reviewed in English for "MathReview" (AMS, USA), since 1999 the journal is reviewed in English for "Zentralblatt fur Matematik" (Berlin, Germany). During 1969-2001 Correspondent Member of NASU P.V. Kharlamov was the Chief-Editor of the journal "Mechanics of rigid body". Correspondent Member of NASU A.M. Kovalev holds this position starting from 2001.

The scientific seminar "Modern problems of dynamics of rigid body, stability and control theory" is weekly held by departments of applied and technical mechanics (Chief A.M.Kovalev). The scientific workers of both departments and others research and educational institutions from Donetsk and all over Ukraine present theirs results on fundamental and applied problems of mechanics.

CONFERENCES

The department of applied mechanics jointly with the department of technical mechanics organized the series of the International Conferences "STABILITY, CONTROL AND RIGID BODIES DYNAMICS". These conferences on general problems in mechanics were held in Donetsk: First (1969), Second (1971), Third (1981), Fourth (1984), Fifth (1990), Sixth (1996), Seventh (1999), Eighth (2002), Ninth (2005), Tenth (2008). Basic scientific schools in the area of mechanics, leading scientific centers of former Soviet Union States and other countries all around the world are presented usually on the conferences.

In 2004 IAMM NASU jointly with Donetsk National University hold the International Conference "Classical problems of rigid body dynamics". It was devoted to 80th anniversary of the birthday of P.V. Kharlamov. The conference was prepared by members of the Organizing Committee: Academicians of NASU I.V. Skrypnik (Chairman), V.P. Shevchenko (Co-Chairman) and A.S.Kosmodamianskiy, Correspondent Members of NASU A.M. Kovalev and A.Ya.Savchenko, doctors of phys.-math. sciences G.V. Gorr, A.A. Iljukhin, M.E. Lesina, candidates of phys.-math. sciences I.N. Gashenenko (Secretary), G.V. Mozalevskaya. During the conference about 70 scientific reports were presented by the leading researches from scientific centres of Ukraine (Kiev, Donetsk, Dnepropetrovsk, Odessa), Russia (Moscow, Volgograd, Ul'yanovsk, Taganrog), Germany (Bremen), Yugoslavya (Belgrad) and others. The section lectures were given by Member of Russian Academy of Sciences V.F. Zhuravlev; Con-Rector of Bremen University, Professor P.H. Richter; Professor of Serbian Mathematical Institute V. Vujichich; Professors A.S. Andreev, A.V.Bolsinov, D.D. Leshchenko, L.G. Lobas, R.G. Mukharlyamov, V.A. Samsonov, V.V. Sokolov, V.N.Tkhai, M.P. Kharlamov and others. The papers presented at the conference reflected the modern state of investigations in analytical mechanics and demonstrated that the research areas formed by P.V. Kharlamov are constantly and successfully developed. The conference presented an evidence of the deep respect of researchers from different countries to P.V. Kharlamov and confirmed the high prestige of Donetsk school of theoretical mechanics originated by him.

In 2007 IAMM NASU jointly with Institute for Problems of Mechanics RAS and Donetsk National University hold the International Conference "Classical problems of rigid body dynamics". It was devoted to 300th anniversary of the birthday of Leonard Euler. Leonard Euler is the outstanding mathematician, mechanician, physicist and astronomer, member of Petersburg and Berlin Academies of Sciences, creator of rigid body dynamics. Submissions to the conference totalled 143 papers from 186 scientists presented 15 countries. Among them 36 were doctors and 30 were candidates of sciences, 34 persons had no a scientific degree including 15 post graduate students. Actually 100 persons took part in the work of the conference, 94 communications were done, 48 participants arrived from another countries: Russia (40), Poland (3), Austria (1), Germany (1), Egypt (1), Canada (1), Romania (1).

INTERNATIONAL COLLOBORATION

The department is taking part in the project "The agreement on collaboration between Institute of Problems of Mechanics of Russian Academy of Science (Moscow, Russia), Donetsk State University and IAMM NASU". The three-way exchange of scientific papers in fundamental and applied problems in theoretical mechanics is actively realized.

The department has the scientific contacts with the chair of differential geometry and applications (Academician of RAS, Professor A.T. Fomenko) and the chair of theoretical mechanics of Moscow State University and Professor A.D. Bruno from Keldysh Institute of Applied Mathematics of RAS (Russia). The joint research is conducted with professor P.H. Richter from Institute of Theoretical Physics of Bremen University (Germany). Professor G.V. Gorr has the scientific contacts with Professor H. Yehia from Mansur University (Egypt). Professor A.O. Ignatyev together with Professor C. Corduneanu from Arlington University (USA) collaborated on the project "Investigation of stability of invariant sets of systems of functional-differential equations with delay" (program COBASE).

The agreement on joint scientific research and educational activities is concluded with the department of applied mechanics of Chendu United University (China). Within this agreement V.F. Shcherbak is contributing into the investigation project "Development of methods and algorithms of solution direct and inverse problems of control of nonlinear dynamical systems with application to dynamics of systems of rigid bodies".

N.V. Khlistunova took part in the project "Dynamical Modelling of Satellite Slew in Maneuvers for Autonomous Small to Medium Size Satellites", Surrey Space Centre, University of Surrey.

MAIN RESULTS

The main scientific results obtained at the department are following:

1. New form of the differential equations and new mathematical models for mechanical systems of rigid bodies are obtained. In particular, the models for a rigid body with a fixed point, a gyrostat, a bundle of rigid bodies coupled by joints, a body on a string, a rigid body with a non-holonomic joint and other systems of holonomic and non-holonomic mechanics were obtained, integrated and qualitatively studied (P.V.Kharlamov, E.I. Kharlamova, I.N.Gashenenko).

2. New method of investigating of invariant relations for constructions of exact solutions for problems of dynamics of rigid body and systems of connected rigid bodies is carried out. Only for classical problem on motion of rigid body with fixed point wh ere up to investigations of applied mechanics department were known 10 solutions named of Euler, Lagrange, Kovalevskaya, Steklov, Chaplygin and others the number of the exact solutions obtained on basis of this method were thrice increased by the research workers of the department. For the first time some new solutions for problems on motions of gyrostat in different fields of forces are found (P.V.Kharlamov, E.I.Kharlamova, A.I. Dokshevich, G.V. Gorr, B.I. Konosevich, E.V.Pozdnyakovich, G.V. Mozalevskaya).

3. With the use of computer graphics tools the method of axoids for visualization of motion is developed. This method gives total information about all singularities of investigated motion (P.V. Kharlamov, M.P. Kharlamov, A.P. Kharlamov).

4. The effective methods of computer analysis and visual representation of complex nonlinear dynamics and topology of integrable problems of classical and modern mechanics are developed. These methods allow to describe a topological structure, to execute the detailed analysis of a behavior of nonlinear mechanical systems and to give the visual geometrical interpretation to many known analytical results ( I.N. Gashenenko).

5. To solve the problems of controllability of nonlinear dynamical systems, the method of oriented manifolds is developed. With its use the algorithms of solution of control problems and inverse problems of identification and invertibillity on the one trajectory and the set of trajectories are obtained (A.M. Kovalev, V.F. Shcherbak).

6. At the results of critical analysis of existing structure of mechanics foundations the new approach to construction of mechanics based on methodology of skeptical empiricism without any myths and metaphysical representations is suggested (P.V. Kharlamov).

Kharlamova E.I.

Pavel Vasilyevich Kharlamov. – Donetsk: IAMM NAS Ukraine, 2001. – 130 p.

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Kharlamov P.V.

Selected Works. – Kiev: Naukova dumka, 2005. – 255 p.

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Gorr G. V., Kudryashova L. V., Stepanova L. A.

Classical problems in the theory of solid bodies. Their development and current state. – Kiev: Naukova Dumka, 1978. – 294 p.
Kharlamova E. I., Mozalevskaya G. V.

An integro-differential equation for the dynamics of a rigid body. – Kiev: Naukova Dumka, 1986. – 296 p.
Dokshevich, A. I.

Closed-form solutions of the Euler-Poisson equations. – Kiev: Naukova Dumka,1992. – 168 p.
Kovalev A.M., Shcherbak V.F.

Controllability, observability, identifiablity of dynamical systems. – Kiev: Naukova Dumka, 1993. – 235 p.
Kharlamov P.V.

Essays on foundations of mechanics. – Kiev: Naukova Dumka, 1995. – 407 p.
Kharlamov P.V.

A critique of some mathematical models of mechanical systems with differential constraints // J. Appl. Math. Mech., 56 (1992), no. 4, P. 584–594.

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Kharlamov P.V.

On the equations of motion of the system of rigid bodies // Rigid Body Mechanics. – 1972. – No. 4. – P. 52-73.

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Kharlamov P.V.

The compound spatial pendulum // Rigid Body Mechanics. – 1972. - No. 4. – P. 73-82.

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Ignatyev A.O.

On the asymptotic stability in functional-differential equations // Proc. Amer. Math. Soc., 127 (1999), no. 6, 1753-1760.

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Gashenenko I.N.

Angular velocity of the Kovalevskaya top. Sophia Kovalevskaya to the 150th anniversary // Regular and Chaotic Dynamics, 5 (2000), no. 1, 107-116.

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Ignatyev A.O.

On the partial equiasymptotic stability in functional differential equations // J. Math. Anal. Appl., 268 (2002), no. 2, 615-628.

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Gorr G.V.

Precession motions in the dynamics of a rigid body and the dynamics of systems of coupled rigid bodies // Prikl. Mat. Mekh., 67 (2003), no. 4, 573-587; translation in J. Appl. Math. Mech., 67 (2003), no. 4, 511-523.

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Gashenenko I.N., Richter P.H.

Enveloping surfaces and admissible velocities of heavy rigid bodies // Int. J. Bifurcation and Chaos, 14 (2004), no. 8, 2525-2553.

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Corduneanu C., Ignatyev A.O.

Stability of invariant sets of functional differential equations with delay // Nonlinear Funct. Anal. Appl. 10 (2005), no. 1, 11-24.

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Bruno A.D., Gashenenko I.N.

Simple exact solutions to the N. Kowalewski equations // Doklady Mathematics, 74 (2006), no. 1, 536-539.

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Ignatyev A.O.

On the stability of invariant sets of systems with impulse effect // Nonlinear Analysis, 69 (2008), no. 1, 53–72.

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Gashenenko I.N., Mozalevskaya G.V., Kharlamova E.I.

On the reduction of the equations of motion of a gyrostat. (Russian) // Rigid Body Mechanics, 38 (2008), 3-19.

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Gashenenko I.N., Gorr G.V., Kovalev A.M.

Classical Problems of the Rigid Body Dynamics. – Kiev: Naukova dumka, 2012. – 402 p. ISBN 978-966-00-1307-0

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Pavel Vasilyevich Kharlamov,

the Founder of the Applied Mechanics Department

Biography

P.V. Kharlamov was born on June 25, 1924 in the village of Gakhovo (Kursk region). Shortly after his birth, the family moved to the city of Donetsk. The Great Patriotic War interrupted his studies in school. In 1946 he served in the Soviet army as a Private soldier of the Guards. For his service in battles, he was awarded with The Order of the Red Star along with several other medals.

In 1947 - 1952 he studied at the Mechanical and Mathematical Faculty of the Moscow State University. Starting his scientific activity at that time, he had chosen to specialize in theoretical mechanics.

In 1952 - 1959 P.V. Kharlamov worked at the Chair of Theoretical Mechanics of Donetsk Industrial Institute. Starting as an assistant lecturer then moving on as a senior lecturer, he finally became the Head of the Chair. In 1955 in Moscow State University, he defended his Candidate of Science (PhD) thesis "A rigid body motion in liquid".

In 1959 - 1965 P.V. Kharlamov worked as a senior research worker in the Institute of Hydrodynamics (Siberian Department of the USSR Academy of Sciences, Novosibirsk). In 1964 he defended the Doctor of Science thesis "On solutions of equations of the rigid body dynamics".

In 1965 P.V. Kharlamov was elected a Correspondent member of the Academy of Sciences of the Ukrainian SSR. At this time the Institute of Applied Mathematics and Mechanics of the Academy of Sciences of the Ukrainian SSR was created, and P.V. Kharlamov left Novosibirsk for Donetsk. Starting from 1965, he was at the head of the Applied Mechanics Department in the Institute. Being one of the organizers of Donetsk Scientific Centre, he took active part in its formation and in the development of fundamental and applied investigations of problems of general mechanics and applied mathematics.

From the very beginning, P.V. Kharlamov planned to create a scientific journal for publishing papers devoted mainly to rigid body dynamics- including the problems of motion of systems of rigid bodies, the problems of analytical mechanics, stability, the control and stabilization of mechanical systems. Such a journal was founded in 1969 as a republican interdepartmental collection of scientific papers entitled "Rigid body mechanics". Issue 1 of this journal was published in 1969, and Issue 39 was published in 2009. Thirty issues of the journal were published during P.V. Kharlamov lifetime, containing 609 papers; most of them came through his hands and mind.

A scientific group created by P.V. Kharlamov performed a number of deep investigations of analytical dynamics and applied problems. This group is well known in the Ukraine and in other countries as The Donetsk School of Mechanics.

In 1976 P.V. Kharlamov joined the USSR National Committee in Theoretical and Applied Mechanics. For a long time he was the head of the Scientific Council for General Mechanics of the Ukrainian Academy of Sciences. Also, he was a member of the Ukrainian National Committee in Theoretical and Applied Mechanics. In 1984 he was awarded the title "Honoured science worker of the Ukrainian SSR".

In 1985, the Victory's anniversary, P.V. Kharlamov was awarded with The First Degree Order of the Great Patriotic War.

In 1996 he was elected as a member of the Academy of Non-linear Sciences.

An outstanding scientist, P.V. Kharlamov was a brilliant lecturer with a deep understanding of the modern requirements to the ways and levels of grounding scientists and engineers. It was particularly important with computerization in all areas of knowledge. His lecture courses in various parts of mechanics were remarkable for their non-traditional construction and for complete mathematical strictness in the union with the wonderful lucidity of explanation.

P.V. Kharlamov is the author of manuals in modern parts of mechanics. Among his disciples, 16 are candidates and 5 are doctors of science. He is the author of 144 scientific works including 5 monographs.

P.V. Kharlamov's scientific interests relate to the wide range of problems of analytical dynamics and continuum mechanics. He got results in the rigid body dynamics, in the multibody system dynamics, in the problem of rigid body spatial motion in liquid and in the problem of motion of a body with cavities filled with liquid, in dynamics of non-holonomic systems. He studied dynamical problems of elasticity theory and examined stability properties of some concrete elastic systems. Also he contributed much to the non-linear system observation problem.

The dynamics of rigid bodies and multibody systems takes the central place in P.V. Kharlamov's investigations. His works in this area of mechanics are of paramount scientific importance; they are remarkable for novelty and profundity of problem definitions, for high constructiveness and effectiveness of investigation methods and for completeness of final results. During the whole period of the rigid body dynamics evolution, numerous attempts were made to find a rational way to describe a body's motion. It is well known that both theorists and engineers confront principal difficulties studying a body's spatial orientation. These difficulties are connected with the necessity to use generalized coordinates describing the rigid body orientation (the Euler angles and their modifications, the Rodrigues - Hamilton parameters, and others). Many ways exist to describe the body spatial orientation, but none of them appears to be universal.

This fact indicates the problem in this field. P.V. Kharlamov has invented a natural (invariant) method for determining the body motion (the hodograph method), which is free of singularities of coordinate methods. His method is based on non-holonomic kinematical characteristics. Corresponding kinematical equations are known in the scientific literature as Kharlamov's equations. In contrast to coordinate methods providing the way to calculate the body's position at given time instant, Kharlamov's method brings the complete solution of the problem: all peculiarities of the body motion can be tracked on the whole time interval. These possibilities were demonstrated in application to the most difficult problems of classical mechanics.

Before Kharlamov's method appearance, construction of exact solutions of the rigid body dynamics equations added up to ascertainment of the phase variables analytical dependence on time (S.V. Kovalevskaya, V.A. Steklov, S.A Chaplygin, and others), and it was of mathematical interest only. Basing on the hodograph method, P.V. Kharlamov and his disciples constructed complete solutions and got all necessary information on all properties of motions in these cases. By now, algorithms are created, which allow fulfilling the most laborious (calculating and graphic) part of construction of the complete solution by computers. The final result is presented as a film clearly demonstrating all peculiarities of the body motion; the result also contains all necessary numerical information about the body position at every required time instant.

The hodograph method is highly important for applications. The natural method of determining the body motion uses only the information about phase variables that can be obtained from sensors placed on the moving object. On the basis of this information, a computer determines the spatial orientation of the body in real time. The prominent result in the rigid body dynamics is a new form of dynamical equations constructed by P.V. Kharlamov. He refused to use the seeming simplicity of the traditional form of the body equations of motion when the angular velocity is presented by its projections on the principal inertia axis for the fixed point. P.V. Kharlamov proposed new dynamical equations referred to special axes, which he introduced. It allowed him to reduce the problem to a comparatively simple system of two differential equations of the first order.

This system is well adapted to investigations by the invariant relations method. P.V. Kharlamov invented this method as a constructive tool to build exact solutions of non-linear systems of differential equations. This method is of great importance both in the theory of differential equations and in solving of concrete applied problems. P.V. Kharlamov and his disciples demonstrated high effectiveness of this method. Previously, different authors had received a restricted amount of exact solutions with intervals measured in dozens of years; each of them was considered as a golden fund in the rigid body dynamics. On the basis of Kharlamov's dynamical equations, many new classes of solutions were obtained in a short period of time. Also a new observation theory for non-linear systems was developed based on the invariant relations method. This theory has important applications to control problems of modern engineering. P.V. Kharlamov generalized S.A. Chaplygin, P.V. Voronets, G.K Suslov and V.V. Vagner statements of problems concerning motion of a rigid body subjected to non-holonomic constraints. His solutions include the corresponding results of these authors as partial cases.

In the problem of motion of a system of connected rigid bodies only two exact solutions were known until recent times; they related to the perfect gyroscope in Cardan suspension. P.V. Kharlamov essentially generalized these results for body systems with more complicated structure and showed integrable cases in other problems of multibody system dynamics (satellite with dual rotation, systems of Lagrange gyroscopes, and others).

In hydrodynamics, P.V. Kharlamov carried out the vast investigations of the problem of rigid body motion in liquid. He proposed a new form of dynamical equations for this problem and generalized Steklov's analogy. At the same time, he did not restrict the body boundary surface to be simply connected. He took into account the liquid circulation flows through apertures and in the body cavities (not simply connected in general). He studied the general cases of stationary (screw) motions and constructed (using the invariant relations method) wide classes of solutions, both new and generalizing classic results by Kirchhoff, Steklov, Lyapunov, Chaplygin, and others.

Under P.V. Kharlamov guidance, stability of motion was investigated for various problems of the rigid body mechanics taking into account their special features. Basing on Kirchhoff - Zhoukovsky analogy, P.V. Kharlamov's disciples modified his kinematical equations for the problem a thin rod bend and torsion. With these equations, new classes of space equilibria of rods had been found. P.V. Kharlamov essentially contributed to Ishlinsky - Lavrentyev problem concerning the longitudinal dynamic bend of a thin rod. Taking into account the possibility of plasticity zones appearance, he found residual forms of rods and established the effect of deformations localization near the end of the blow impulse application. He found out a similar effect in the problem of residual supercritical forms of cylindrical shell under action of axial compressive impulse. An interesting cycle of P.V. Kharlamov's works deals with the problem of motion of a rotating body suspended by a string. He solved the problem (of nearly 50 years history) of stability for the first form of the body steady motion. A new mathematical model covering non-holonomic suspensions, dissipation in the system and the existence of an engine was proposed. Discrepancies between experimental results and results predicted by the earlier proposed mathematical models were removed. In his works, P.V. Kharlamov compared and critically analysed the existing methodologies in various mathematical models in rigid body dynamics beginning from the original works of Galileo, Hamilton, and Lagrange. He demonstrated the principal differences and their influence on the problems of dynamics and, in particular, on the problem of motion of a rigid body suspended by a string. Applying the modern computer tools ensured the possibility to obtain the results necessary for such analysis, both in numerical and in graphical form.

In 1985, P.V. Kharlamov published the monograph entitled "Foundations of Newtonian mechanics". It is known that the fundamental notions of Newtonian mechanics were always accompanied by discussions. P.V. Kharlamov thought that the reasons of these discussions relate to the personal subjective element, which every researcher brings into the model of mechanical motion. P.V. Kharlamov considered such notions as space, time and force from modern positions. He discovered the possibility to construct the foundations of mechanics based only on the notion of a material body and addressed to specialists in applied mechanics.

Up to his last days, P.V. Kharlamov was engaged in the problems of foundations of mechanics, philosophy and methodology of science, questions of cognition. Two papers by P.V. Kharlamov are published in Issue 30 of "Rigid body mechanics", the last issue appeared at his life. The title of the first paper was "Galileo is the founder of mechanics". From modern positions, the role of Galileo is characterized as a creator of mechanics, the science about motion. Galileo's merit was distinguished in creating modern methodology of investigation of nature phenomena. The central role of experiment was emphasized together with significance of the critical analysis of introduced hypotheses and obtained results. Such way of investigation is the only way that P.V. Kharlamov has followed in all his creative work. The second work was entitled "The modern state and the developing perspectives for classic problems of rigid body dynamics". In this paper, P.V. Kharlamov presented his point of view on the directions of progress in dynamics, emphasizing and highly estimating the global computer influence on the further development of mechanics and mathematics.

In February 2001, Presidium of the National Academy of Sciences of Ukraine awarded P.V. Kharlamov (together with two colleagues) with Krylov Prize for the cycle of publications in mathematical problems of analytical mechanics.

By P.V. Kharlamov's initiative, scientific conferences on problems of rigid body dynamics started to be hold in Donetsk beginning from 1969. In September 2002, the Eighth International conference "Stability, control and rigid body dynamics" was hold devoted to the memory of P.V. Kharlamov.

P.V. Kharlamov passed away due to heart illness on March 16, 2001. The outstanding scientist, creator of Donetsk School of Mechanics left this world.
Kharlamov Pavel Vasilyevich

On various presentations of Kirchhoff equations // Rigid Body Mechanics. – No. 31. – Pp. 3-17. (co-authors G.V. Mozalevskaya, M.E. Lesina)

A case of integrability of the equations of motion of a heavy rigid body in a fluid. (Russian) Prikl. Mat. Meh. 19, (1955). 231--233.

On an estimate for the solutions of a system of differential equations. (Russian) Ukrain. Mat. Ž. 7 (1955), 471--473.

Translational motion of a heavy rigid body in a fluid. (Russian) Prikl. Mat. Meh. 20 (1956), 124--129.

Integrable cases in the problem of motion of a heavy solid body in a fluid. (Russian) Dokl. Akad. Nauk SSSR (N.S.) 107 (1956), 381--383.

On linear integrals of the equations of motion of a heavy solid body about a fixed point. Dokl. Akad. Nauk SSSR 143 805--807 (Russian); translated as Soviet Physics Dokl. 7 1962 308--309.

A particular case of integrability of the equations of motion of a gyrostat. (Ukrainian) Dopovīdī Akad. Nauk Ukraïn. RSR Ser. A1969 1969 1104--1106, 1151. (Co-author L. M. Kovalʹova)

New methods for the study of problems in the dynamics of a rigid body. (Russian) Problems in analytical mechanics, stability and control theories (Second Četaev Conf., Kazan, 1973) (Russian), pp. 317--325, 343. Izdat. ``Nauka'', Moscow, 1975.

A study of the solution with two linear invariant relations of the problem of the motion of a body with a fixed point (special cases). (Russian) Meh. Tverd. Tela Vyp. 8 (1976), 37--56, 138.

Some questions on the nonlinear theory of the observation of dynamical systems. (Russian) Dokl. Akad. Nauk Ukrain. SSR Ser. A 1977, no. 3, 244--247, 286. (Co-authors G. V. Gorr, A. I. Doksevic, A. M. Kovalev, B. I. Konosevich, A. Ja. Savcenko)

Separating motions of a Lagrange gyroscope. (Russian) Mekh. Tverd. Tela No. 11 (1979), 17--22, 118.

An exact solution for the problem of motion of the Lagrange two-gyroscope system. (Russian) Dokl. Akad. Nauk Ukrain. SSR Ser. A 1981, no. 4, 50--52, 97. (Co-author M. E. Lesina)

Supercritical forms of a thin circular cylindrical shell under axial compression. (Russian) Mekh. Tverd. Tela No. 12 (1980), 92--96, 120. (Co-author V. A. Karagʹozov)

On the equations of motion for a heavy body with a fixed point. Prikl. Mat. Meh. 27 703--707 (Russian); translated as J. Appl. Math. Mech. 271964 1070--1078.

A solution for the motion of a body with a fixed point. Prikl. Mat. Meh. 28 158--159 (Russian); translated as J. Appl. Math. Mech. 28 1964 185--187.

Kinematic interpretation of the motion of a body with a fixed point. Prikl. Mat. Meh. 28 502--507 (Russian); translated as J. Appl. Math. Mech.28 1964 615--621.

Polynomial solutions of the equations of motion of a body with a fixed point. Prikl. Mat. Meh. 29 26--34 (Russian); translated as J. Appl. Math. Mech. 29 1965 26--35 (1966).

New methods in the dynamics of systems of rigid bodies. Dynamics of multibody systems (Proc. IUTAM Sympos., Munich, 1977), pp. 133--143, Springer, Berlin-New York, 1978.

The value of geometrical methods in problems of the dynamics of a rigid body. (Russian) Stability of motion. Analytical mechanics. Control of motion, pp. 265--274, 304, ``Nauka'', Moscow, 1981.

The motion of the Kovalevskaya gyroscope in the Delone case. (Russian) Mekh. Tverd. Tela No. 14 (1982), 38--54, 130. (Co-author V. I. Kovalʹ)

Some classes of exact solutions of the problem of the motion of a system of Lagrange gyroscopes. (Russian) Mat. Fiz. No. 32 (1982), 63--76.

Some classes of exact solutions of a problem on the motion of two connected bodies. (Russian) Dokl. Akad. Nauk Ukrain. SSR Ser. A 1983, no. 3, 53--54. (Co-author M. E. Lesina).

To solve a problem of rigid body dynamics. What does it mean? Proceedings of the IUTAM-ISIMM symposium on modern developments in analytical mechanics, Vol. II (Torino, 1982). Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 117 (1983), suppl. 2, 535--562. (Co-author M. P. Kharlamov)

Why do physicists argue about the foundations of mechanics? (Russian) With an afterword by A. Yu. Ishlinskiĭ and a comment by I. S. Alekseev. Studies in the the history of physics and mechanics, 1989 (Russian), 186--211, ``Nauka'', Moscow, 1989.

Mechanics and relativity theory. (Russian) Ocherki Istor. Estestvoznan. Tekhn. No. 38 (1990), 16--24.

Commentaries to a paper of L. A. Stepanova: ``An unsuccessful attempt to defend the priority of the classics of Russian mechanics in constructing exact solutions in the mechanics of a rigid body'' [Mekh. Tverd. Tela No. 22 (1990), 19--33] and of A. I. Khokhlov: ``An unsuccessful attempt to defend a result of V. A. Steklov'' [Mekh. Tverd. Tela No. 23 (1991), 26--36; MR1160719 (93g:01039)]. (Russian) Mekh. Tverd. Tela No. 23 (1991), 36--43.

How L. I. Sedov interprets Newtonian mechanics. (Russian) Mekh. Tverd. Tela No. 23 (1991), 61--78.

A critique of some mathematical models of mechanical systems with differential constraints. (Russian) Prikl. Mat. Mekh. 56 (1992), no. 4, 683--692; translation in J. Appl. Math. Mech. 56 (1992), no. 4, 584--594.

Constraints and reactions. (Russian) Mekh. Tverd. Tela No. 24 (1992), 95--103.

On the correspondence to an experiment of the essential theories of motion of a suspended body. (Russian) Mekh. Tverd. Tela No. 26, part I, II (1994/98), 96--111.

Contradictions in the principles of mechanics. (Russian) Facta Univ. Ser. Mech. Automat. Control Robot. 2 (1996), no. 6, 163--168.

Causes of contradictions in the principles of mechanics (Galilei and Newton). (Russian) Facta Univ. Ser. Mech. Automat. Control Robot. 2(1996), no. 6, 169--180.

Possibilities for removing contradictions in the principles of mechanics. (Russian) Facta Univ. Ser. Mech. Automat. Control Robot. 2 (1996), no. 6, 181--187.

Invariant relations method in multibody dynamics. Proceedings of the Second World Congress of Nonlinear Analysts, Part 6 (Athens, 1996). Nonlinear Anal. 30 (1997), no. 6, 3817--3828. (Co-author A. M. Kovalev).

The current state of the classical problems of the dynamics of a rigid body and prospects for their development. (Russian) Mekh. Tverd. TelaNo. 30 (2000), 1--13.

Galileo---the founder of mechanics. (Russian) Mekh. Tverd. Tela No. 30 (2000), 258--283.

Various representations of the Kirchhoff equations. (Russian) Mekh. Tverd. Tela No. 31 (2001), 3--17. (Co-authors G. V. Mozalevskaya, M. E. Lesina).

Hodographs of angular velocity of Mme. Kovalevskaja's gyroscope in the Delone case. (Russian) Mekh. Tverd. Tela No. 11 (1979), 3--17,118. (Co-author
V.I. Kovalʹ).

On some motions of a system of three Lagrange gyroscopes. (Russian) Mekh. Tverd. Tela No. 14 (1982), 76--82, 131. (Co-author M. E. Lesina).

Cases of integrability of the equations of integral motion of two bodies joined by a spherical linkage. (Russian) ; translated fromIzv. Akad. Nauk SSSR Mekh. Tverd. Tela 18 (1983), no. 4, 26--31 Mech. Solids 18 (1983), no. 4, 22--28 (Co-author M. E. Lesina).

2010

1. Gorr G.V., Maznev A.V. Dynamics of a Gyrostat Having a Fixed Point. –Donetsk Nat. Uni., 2010. – 364 p.
2. Gashenenko I.N. Poinsot kinematic representation of the motion of a rigid body in the Hess case // Rigid Body Mechanics. – 2010. – No. 40. – P. 12-20.
3. Gashenenko I.N. Perturbed pendulum-like motions of a rigid body about a fixed point // Rigid Body Mechanics. – 2010. – No. 40. – P. 34-49.
4. Ignatyev A.O. On existence of the quadratic Lyapunov function for linear systems of differential equations with impulse effect // Ukrainian Mathematical Journal. – 2010. – 62, No. 11. – P. 1451-1458.
5. Shcherbak V.F. Stabilization of the pendulum system // Rigid Body Mechanics. – 2010. – No. 40. – P.197-201.
6. Konosevich Yu.B. Investigation of the gimbal mounted synchronous gyroscope drift rate dependence of the inner frame swivel angle // Rigid Body Mechanics. – 2010. – No. 40. – P. 125–135.
7. Volkova O.S. Regular precession of a gyrostat with fixed point in the gravitational field // Rigid Body Mechanics. – 2010. – No. 40. – P. 63–76.
8. Volkova O.S., Gashenenko I.N. Pendulum-like motions of a gyrostat with a variable gyrostatic momentum // Proc. Ukrainian Mathematical Congress – 2009, Section 1. – Kyiv, Institute of Mathematics of NASU. – 2010. – P.40–51.
9. Lesina M.E., Gogoleva N.F. Equations of hodographs in the reference basis for the problem of inertial motion of two Lanrange gyros jointed by a nonholonomic hinge // Rigid body mechanics. – 2010. – No. 40. – P. 112-124.

10. Velmagina N.A., Verbitskii V.G. The bifurcation set for a two-axes vehicle with the non-monotone dependence of sllipping forces // Rigid Body Mechanics. – 2010. – No. 40. – P. 136-143.

11. Verbitskii V.G., Khrebet V.G., Velmagina N.O. The bifurcation set for a two-axes vehicle model with the non-linear dependence of slipping forces // Proc. Int. Conf. on Nonlinear Dynamics, Kharkov, 2010.

– P. 219-224.

12. Ignatyev A.O. Quadratic forms as Lyapunov functions in the study of stability of solutions to difference equations // Electron. J. Differential Equations, Vol. 2011 (2011), No. 19.

– P. 1-21.

13. Ignatyev A.O. Comments on "On stability of switched homogeneous nonlinear systems" by Lijun Zhang, Sheng Liu, and Hai Lan [J. Math. Anal. Appl. 334 (2007) 414-430] //

J. Math. Anal. Appl.– 337, 2011.– P. 343-344.

2009

1. Chebanov D., Kovalev A.M., Bolgrabskaya I.A., Shcherbak V.F. On the Usage of Dynamic Vibration Absorbers for Reduction of Forced Vibrations of a System of Coupled Rigid Bodies // Proc. of the ASME 2009 Intern. Design Engineering Technical Conferences. San Diego, CA, USA (August 30 – September 2, 2009): Paper DETC2009–87731. – P. 143–154.
2. Gashenenko I.N. On the D.N. Goryachev solution // Rigid Body Mechanics. – 2009. – No. 39. – P. 31-37.
3. Gorr G.V., Zyza A.V. On reduction of differential equations in two problems of rigid body dynamics // Proceedings of the Institute of Applied Mathematics and Mechanics. – 2009. – 18. – P. 29-36.
4. Gorr G.V., Maznev A.V., Shchetinina E.K. Precession motions in rigid body dynamics and in dynamics of system of coupled   rigid   bodies . – Donetsk: Donetsk National University. – 2009. – 222 p.
5. Ignatyev, Alexander O.; Ignatyev, Oleksiy A.   Stability of solutions of systems with impulse effect. – Progress in nonlinear analysis research. – New York: Nova Sci. Publ. – 2009. – P. 363-389
6. Ignatyev A.O. Lyapunov's second method in problems of the stability of solutions of systems with impulse effect // Proc. in Appl. Math. & Mech. – Vol. 7. – 2009. – P. 2030031–2030032.
7. Kovalev A.M., Kozlovskii V.A., Shcherbak V.F. Generalized reversibility of dynamical systems in encryption problems // Applied   discrete mathematics. – 2009. –   No. 1. – P. 20–21.
8. Shcherbak V.F. Determination of the angular velocity vector by its projection // Rigid body mechanics. – 2009. – No. 39. – P. 171-180.
9. Volkova O.S., Gashenenko I.N. The pendulum rotations of a heavy gyrostat with variable gyrostatic momentum // Rigid Body Mechanics. – 2009. – No. 39. – P. 42-49.

2008

1. Gashenenko I.N., Mozalevskaya G.V., Kharlamova E.I. On the reduction of equations of the gyrostat   motion // Rigid Body Mechanics. – 2008. – No 38. – P. 3-19.
2. Gorr G.V., Mironova E.M. On asymptotically precessional motions of a spherical gyrostat in the case of semiregular precession of the first type //   Rigid Body Mechanics. – 2008. – No. 38. – P. 1-8.
3. Ignatyev A. O. On the equiasymptotic stability of solutions of doubly periodic systems with impulse action // Ukraïn. Math. J. – 2008. – 60, No. 10. – P. 1317–1325.
4. Ignatyev, Alexander O. On the stability of invariant sets of systems with impulse effect // Nonlinear Analysis. – 2008. – 69, No. 1. – P. 53-72.
5. Ignatyev, Alexander O.; Ignatyev, Oleksiy A. Investigation of the asymptotic stability of solutions of systems with impulse effect // Int. J. Math. Game Theory Algebra. – 2008. –  17,   No . 3. – P. 141-164.
6. Ignatyev A. O. Asymptotic stability and instability with respect to part of the variables of solutions of systems with impulse action // Siberian Math. J. – 2008. – 49, No. 1. – P. 125–133.
7. Ignatyev A.O. Lyapunov's second method in problems of the stability of solutions of systems with impulse effect // Proceedings in Applied Mathematics and Mechanics. – 2008. –   P. 2030031-2030032.
8. Kovalev A.M., Kozlovskii V.A., Shcherbak V.F. Reversible dynamical systems with variable dimension of the phase space in problems of cryptographic transformation of information // Applied   discrete   mathematics. – 2008. –   No. 2 (2). – P. 39–44.
9. Konosevich B.I., Konosevich Yu.B. Model of the electric engine in the gyroscope theory // Proceedings of the Institute of Applied Mathematics and Mechanics. – 2008. – 17. – P. 88-95.
10. Shcherbak V.F. Synchronization of angular velocities of gyrostats // Rigid Body    Mechanics. – 2008. – No. 38. – P. 56-60.

2007

1. Bolgrabskaya I.A., Konosevich Yu.B. Stability of pseudoregular precessions of the gimbals suspended synchronous gyroscope having a dynamically asymmetrical rotor // Proceedings of the Institute of Applied Mathematics and Mechanics. – 2007. – 14. – P. 30-40.
2. Gashenenko I.N., Mozalevskaya G.V., Kharlamova E.I. On the reduction of Euler- Poisson equations // Rigid Body Mechanics. – 2007. – No 37. – P. 69-84.
3. Gladilina R. I., Ignatyev A. O. On the preservation of the stability property of impulsive systems under perturbations // Automat. i Telemekh. – 2007, No. 8. – P. 78-85.
4. Gorr G.V., Shchetinina E.K. On integrating factor for equations of rigid body dynamics on invariant manifolds // Reports of Academy of Sciences of the Ukrainian SSR. – 2007. – No. 1. – P. 60-66.
5. Kovalev A.M., Kozlovskii V.A., Shcherbak V.F. Information transformation dynamical systems with variable dimension of the phase space // Proceedings of the Institute of Applied Mathematics and Mechanics. – 2007. – 14. – P. 98-107.
6. Kovalev A.M., Savchenko A.Ya., Kozlovskii V.A., Shcherbak V.F. Reversion of input-output dynamical systems in information security problems // Artificial intelligence. – 2007. – No. 4. – P. 416–424.

2006

1. Bolgrabskaya I.A., Konosevich Yu.B. Influence of the dynamic asymmetry of the rotor on stationary motions of the synchronous gyroscope in gimbals // Proceedings of the Institute of Applied Mathematics and Mechanics. – 2006. – 13. – P. 12-18.
2. Bruno A.D., Gashenenko I.N. Simple exact solutions to the N. Kowalewski equations // Doklady Mathematics. – 2006. – 74, No. 1. – P. 536-539.
3. Gashenenko I.N. Isoenergy surfaces in the problem on motion of a rigid body about a fixed point. // Rigid Body Mechanics. – 2006. – No 36. – P. 3-12.
4. Gorr G.V., Shchetinina E.K. New classes of precessional motions of a gyrostat under the action of potential and gyroscopic forces // Proceedings of the Institute of Applied Mathematics and Mechanics. – 2006. – 12. – P. 35-45.
5. Ignatyev A.O., Ignatyev O.A. On the stability in periodic and almost periodic difference systems // J. of Math. Analysis and Applications. – 2006. – 313. – P. 678-688.
6. Ignatyev A.O, Ignatyev O.A., Soliman A.A. Asymptotic stability and instability of the solutions of systems with impulse action // Mathematical Notes. – 2006. – 80, No. 4. – Р. 491-499.
7. Ignatyev A.O., Ignatyev O.A. On the stability in discrete systems // In book "Integral Methods in Science and Engineering". – Birkhauser, 2006. – Р. 74-78.
8. Konosevich B.I., Konosevich Yu.B. Asymptotic behaviour of perturbed steady motions of the synchronous gyroscope in gimbals // Mech. of Rigid Body. – 2006. – No. 36. – P. 64–74.
9. Shcherbak V.F. Identification of perturbations acting on the gyroscope // Mech. of Rigid Body. – 2006. – No. 36. – P. 90–93.

2005

1. Bruno A.D., Gashenenko I.N. Finite solutions of the N. Kowalewski equations // Rigid Body Mechanics. – 2005. – No. 35. – P. 31-37.
2. Gashenenko I.N. The integral manifolds of the problem on motion of an asymmetrical gyrostat. // Proceedings of the Institute of Applied Mathematics and Mechanics. – 2005. – 10. – P. 24-31.
3. Gashenenko I.N. Bifurcations of the integral manifolds in the problem on motion of a heavy gyrostat // Nonlinear dynamics. – 2005. – 1, No.1. – P. 33-52.
4. Gorr G.V., Uzbek Ye.K. On a new solution to Kirchhoff equations in the case of linear invariant relation // Applied Mathematics and Mechanics. – 2005. – 67, No. 6. – P. 931-939.
5. Gorr G.V., Yahya H.M., Shchetinina E.K. On integration of the Grioli equations in the case of one linear invariant relation // Rigid Body Mechanics. – 2005. – No. 35. – P. 49-57.
6. Ignatyev A.O. Investigation of stability using Lyapunov functions with constant   signs // Ukr. Mat. Visn. – 2005. – 2, No. 1. – P. 61-70.
7. Kovalev A.M., Gashenenko I.N., Kirichenko V.V. On chaotic motions and separatrices splitting of the perturbed Hess motion // Rigid Body Mechanics. – 2005. – No. 35. – P. 19-30.
8. Konosevich B.I. On equations of motion of the shell written in V.S. Pugachev form // Mech. of Rigid Body. – 2005. – No. 35. – P. 73-83.
9. Konosevich B.I. Mass point model in the the flight theory of a projectile // Proceedings of the Institute of Applied Mathematics and Mechanics. – 2005. – 10. – P. 98–107.
10. Konosevich Yu.B. Stability criterion for steady motions of the synchronous gyroscope in   gimbals // Mech. of Rigid Body. – 2005. – No. 35. – P. 115-123.
11. Corduneanu C., Ignatyev A.O. Stability of invariant sets of functional differential equations   with delay // Nonlinear Functional Analysis and Applications. – USA. – 2005. – 10, No. 1. – P. 11-24.
12. Kharlamova E.I., Mozalevskaya G.V. Rigid body dynamics during 40 years in the Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine // Science and research on research . – No. 4. – P. 110-127.
13. Kharlamova E.I., Mozalevskaya G.V. 40 years anniversary of Donetsk school of analytical mechanics // Scientific works of Donetsk National techological university. – 2005. – 94. – P. 13-34.
14. Kharlamov P.V. Selected works. – Kiev: Naukova Dumka. – 2005. – 255 p.
15. Shcherbak V.F. Synthesis of invariant relations in the observation problem of a body angular velositry // Rigid Body Mechanics. – 2005. – No. 35. – P. 224-228.

2004

1. Ignatyev A.O. Asymptotic Stability in Functional Differential Equations with Delay // In book "Integral Methods in Science and Engineering" (Editors: C.Constanda, M.Ahues,  and A.Largillier). Birkhauser. – 2004. – P. 97-102.
2. Ignatyev A. O. On the stability of the zero solution of an almost   periodic system of difference equations. // Differential equations. – 2004. – 40, No. 1. – P. 98-103.
3. Kovalev A.M, Bolgrabskaya I.A., Shcherbak V.F.   Damping of   Manipulator Forced Oscillations as Control Problem   for   Underactuated Multibody   // 49   Internationales  Wissenschaftliches Kolloquium “Synergies between   Information and    Automation”. Ilmenau (Germany): Shaker Verlag, – 2004. – 1. – P. 163-170.
4. Gorr G.V., Uzbek E.K. Fractionally linear integral of Poisson equations in the case of three invariant relations // Problems of nonlinear analysis in engineering systems.– Kazan. – 2004. – 10, No. 2. – P. 54-71.
5. Gladilina R. I., Ignatyev A. O. On the stability of periodic systems with impulse action // Mathematical Notes. – 2004. – 76, No. 1. – P. 44-51.
6. Gashenenko I.N., Richter P.H. Enveloping surfaces and admissible velocitiesof heavy rigid bodies // Int. J. of Bifurcations and Chaos. – 14, No. 8. – P. 2525-2553.
7. Gashenenko I.N. Bifurcations of levels of the first integrals in the problem on motion of a gyrostat with a fixed point // Rigid Body Mechanics. – 2004. – No. 34. – P. 37-46.
8. Gladilina R.I. Lyapunov functions method in stability problems with respect to part of the variables for impulsive systems // Visn. Kiev Univ. Kibernetika. – 2004. – No. 5. – P. 4-7.

2003

1. Kharlamova E.I. Donetsk school of mechanics is the successor and continuer of classic native mechanics // Science and research on research. – 2003. – No. 4.
2. Kovalev A.M., Bolgrabskaya I.A., Shcherbak V.F. Damping of forced oscillations in the linked rigid bodies systems // International Applied Mechanics. – 2003. – 39 (49), No. 3. – P. 110-117.
3. Gorr G.V. Precessional motions in rigid body dynamics and in dynamics of a system of coupled rigid bodies // Applied Mathematics and Mechanics. – 2003. – 67, No. 4. – P. 573-587.
4. Barteneva I.V., Cabada A.O., Ignatyev A.O. Maximum and anti-maximum principles for the general operator of second order with variable coefficients // Applied Mathematics and Computation. – 2003. – 134. – P. 173-184.
5. Konosevich B., Konosevich Yu. Investigation of the stability conditions for the stationary motions of gyro in Cardan suspension, supplied with the electric engine // Proc. 7-th Сonference on Dynamical Systems Theory and Applications. – Lódź, December 8-10, 2003. – P. 337-344.
6. Konosevich B.I. Investigation of the main stability condition for stationary motions of the gyroscope in Cardanic suspension, supplied with the electric engine // Rigid Body Mechanics. - 2003. - No. 33. - P. 80-89.
7. Savchenko A.Ya., Kovalev A.M., Kozlovskii V.A., Shcherbak V.F. Inverse dynamical systems in secure communication and its discrete analogs for information transfer // Proc. of 2003 Workshop of Nonlinear Dynamics of Electronic Systems (NDES 2003, Scuol/Schuls Switzerland). – 2003. – P. 225-228.
8. Gashenenko I.N. Integral manifolds in the problem on motion of a heavy rigid body // Rigid Body Mechanics. – 2003. – No 33. – Pp. 20-32.
9. Gladilina R. I., Ignatyev A. O. On necessary and sufficient conditions for the asymptotic stability of impulsive systems // Ukrainian Mathematical Journal. – 2003. – 55, No. 8. – P. 1035-1043.
10. Kovalev A.M., Shcherbak V.F. Inverse control systems in problems of information security // Artificial intelligence. – 2003. – No. 4. – P. 41-50.
11. Shcherbak V.F. Synthesis of virtual measurements in nonlinear observation problem // Artificial intelligence. – 2003. – No. 3. – P. 57-69.
12. Khlistunova N.V. Spectra of symplectic integration mappings for a nearly axisymmetric rigid body with a fixed point moving free // Rigid Body Mechanics. – 2003. – No. 33. – P. 194-203.
13. Bolgrabskaya I.A., Konosevich B.I., Yakovenko V.T. Influence of an asymmetry in movers arrangement on stability of hovering mode of an aircraft // Rigid Body Mechanics. – 2003. – No. 33. – P. 109 –118.
14. Shcherbak V.F. State tracking problem for nonlinear system under incomplete information about motion // Rigid Body Mechanics. – 2003. – No. 33. – P. 127-132.
15. Bernfeld S., Corduneanu C., Ignatyev A.O. On the stability of invariant sets of functional differential equations // Nonlinear Analysis. – 2003. – 55. – P. 641-656.

2002

1. Kharlamova E.I. Pavel Vasilyevich Kharlamov. Biography and index of scientific works. – Donetsk: Publication of the Institute of Applied Mathematics and Mechanics NASU. – 2002. – 15 p.
2. Kovalev A.M., Zuev A.L., Shcherbak V.F. The synthesis of stabilizing control for a rigid body with jointed elastic elements // Journal of automation and information sciences. – 2002. – 33, No. 6. – P. 5-17.
3. Gorr G.V., Uzbek Ye.K. Integration of Poisson’s equations in the case of three linear invariant relations // Applied Mathematics and Mechanics. – 2002. – 66, No. 3 – P. 418-426.
4. Gashenenko I.N. Enveloping surfaces in the problem on motion of a heavy gyrostat // Rigid Body Mechanics. – 2002. – No 32. – P. 39-49.
5. Gashenenko I.N., Kucher E.Yu. Characteristic exponents of periodic solutions of the Euler-Poisson equations // Rigid Body Mechanics. – 2002. – No. 32. – P. 50-59.
6. Shcherbak V.F. Inverse system use in control problems // Proceedings of the Institute of Applied Mathematics and Mechanics. – 2002. – 7. – P. 229-235.
7. Konosevich B.I. Error estimation for the classic integrating scheme of equations of motion of the axisymmetric projectile // Mech. of Rigid Body. – 2002. – No. 32. – P. 88-98.

2001

1. Kharlamov P.V., Mozalevskaya G.V., Lesina M.E. On various representations of Kirchhoff's equations // Rigid Body Mechanics. – 2001. – No. 31. – P. 3-17.
2. Kharlamova E.I. Pavel Vasil’evich Kharlamov. – Donetsk: Publication of the Institute of Applied Mathematics and Mechanics NASU. – 2001. – 144 p.
3. Kudryashova L.V., Mozalevskaya G.V. Geometric images of Kovalevskaya top motion // History and methodology of science. Intercollege collection of scientific works. – Perm: Perm. Univ. Publishing. – 2001. – No. 8. – P. 230-238.
4. Gashenenko I.N., Kucher E.Yu. Analysis of isoenergy surfaces for exact solutions of the problem on a rigid body motion // Rigid Body Mechanics. – 2001. – No. 31. – P. 18-30.
5. Shcherbak V.F. Inverse systems in the observation problem of uncertain systems // Mechanic of Rigid Body. – 2001. – No. 31. – P. 134-139.
6. Khlistunova N., Chebanov D. To the question on permanent rotations of the rigid bodies system // Proceedings of the Institute of Applied Mathematics and Mechanics. – 2001. – 6. – P. 153-158.
7. Khlistunova N., Chebanov D. On conditions of existence of permanent rotations of the connected rigid bodies system about the vercal vector // Facta Universitatis, Ser.: Mech., Autom. Control and Robotics. – 2001. – 3, № 11. – P. 71-79.
8. Gorr G.V. On one class of precessionaly isoconical motions of a rigid body under the action of potential and gyroscopic forces // Rigid Body Mechanics. – 2001. – No. 31. – P. 31-37.

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