Stability, control and rigid bodies dynamics
10th International Conference
(Ukraine, June, 2008)
A.M.Kovalev, B.I.Konosevich
Institute of Applied
Mathematics and Mechanics of Ukraine NAS
Str. 74, R.Luxemburg, Donetsk, 83114, Ukraine
By the initiative of Professor P.V.Kharlamov,
who is the founder of Donetsk school of analytical mechanics, beginning
1969 the Institute of applied mathematics and mechanics of the National Academy
of Sciences of Ukraine (IAMM NASU) holds conferences on the
actual problems of rigid bodies' dynamics, stability theory and control theory. The subject-matter of these conferences is connected
with modern researches in the field of general mechanics and applied
mathematics. It includes the modern technical objects modelling by rigid bodies
systems, construction of new mathematical methods for investigation of dynamics
of complete mechanical systems, elaboration of the effective ways for control
of moving objects, further development of the stability theory, and application
of general methods to investigation of dynamics of different objects. The
number of participants of these conferences is 100-150 persons, and it allows
to discuss the problems in details and to establish close contacts between
scientific schools. At present time, these conferences take place with regularity
once in three years.
The regular 10th
International conference "Stability, control and rigid bodies' dynamics" was
held by IAMM NASU on June
5-10, 2008. Its organization was fulfilled by
the departments of applied and technical mechanics of IAMM NASU and by the
mathematical faculty of Donetsk National University (DonNU). DonNU lent a great help
in the material security of the conference. The boarding-house "Nauka", situated on Azov sea
coast in 15 km
distance from Mariupol, was put by DonNU as the conference place. The conference was supported
materially by the company "BMS consulting" (Kiev).
Submissions to
the 10th conference totaled 130 papers from 174 authors. Among them
28 were doctors and 25 were candidates of sciences, 38 persons were from Ukraine.
Actually 82 persons took part in the work of the Conference, they arrived from
9 countries (Ukraine, Russia, Armenia, Byelorussia, Egypt, France, Japan, Poland, Serbia).
They presented 87 communications including 11 plenary lectures, 15 section
lectures, 42 short talks in sections and 19 posters. Selected works are published
in the collection of scientific papers (IAMM NASU).
Some survey of plenary lectures.
S.A.Dovgii, V.V.Meleshko
and A.N.Trofimchuk (Ukraine) presented a lecture , which exited a great interest. The
authors informed about modern possibilities for search of the scientific
information and gave some recommendations especially useful for scientists from
the former Soviet
Union.
V.A.Samsonov presented the
plenary lecture of M.Z.Dosaev, L.A.Klimina,
B.Ya.Lokshin (Russia) entitled
, where a mathematical model was developed for an energy plant
consisting of the electric generator and the wind turbine. Evolution of the
stable periodic regimes was studied depending on parameters.
K.Hedrih presented a
lecture . This lecture
contained a survey of the author's research results on dynamical models of
mechanical systems consisting of the great number of coupled deformable bodies.
M.P.Kharlamov (Russia) presented
his work Kovalevskaya
gyrostat in two constant fields>, where the equations of the stratified
critical set of the integral map were obtained for the gyrostat. All critical periodic
motions of the Kovalevskaya gyrostat in two constant
fields were found explicitly.
In the lecture
Sommerfeld-Kononenko effect
study>, T.S.Krasnopolskaya (Ukraine)
told about investigations of the coupling effect between an excitation machine
and vibrational load.
S.M.Onyshchenko (Ukraine) presented
the lecture ,
where direct, reverse and semireverse synthesis
methods were examined.
V.S.Sergeev (Russia) made a report entitled
integrodifferential equations of Volterra-type>.
The stability under persistent disturbances and the structure of the general
solution were investigated in the neighborhood of zero assuming asymptotic
stability of the trivial solution of the linearized unperturebed equation. Stability properties in two critical
cases were analyzed too.
In the plenary lecture <Integrable matrix ODEs> of V.V.Sokolov (Russia), a number of integrable classes of nonlinear matrix ordinary
differential equations were constructed. This type equations
describe, in particular, n-dimentional rigid body dynamics.
In the lecture of V.N.Tkhai (Russia) entitled photogravitational three-body problem: libration
points and stable agglomerations of microparticles> the
author's results were presented concerning the stable agglomerations of microparticles in the double star system.
H.Yabuno, A.A.Mailybaev
and A.P.Seyranian (Japan, Russia) presented their work . They showed a film where experiments were demonstrated that
connected with stability and stabilization of equilibrium positions of a
physical pendulum with vibrating suspension point and of an elastically
supported beam of variable width under the action of periodic axial forces. The
experimental data were compared with the theoretical results of the authors.
In the work of H.M.Yehia (Egypt) entitled
time-irreversible systems with Lagrangians involving
terms linear in velocities were investigated. Two sets of these type integrable systems were constructed in addition to the
previous results of the author.
Not long ago D.L.Abrarov (Russia) published two
books and V.N.Onikiychuk (Russia) published one
book containing the authors results that give, by
their opinion, the exact solution of the problem on motion of a rigid body with
a fixed point in the field of gravity. This problem is one of the classical
problems of mechanics and it is one of the main topics of the conference series
"Stability, control and rigid bodies dynamics".
Therefore the scientific community presented at the 10th Conference
had to express its attitude to these publications. For this purpose the Round
Table discussion was hold on the theme "Integrability
problem for equations of rigid body dynamics". It was organized in the
following way: at first D.L.Abrarov and V.N.Onikiychuk told about their results, and then the
consideration of the theme took place. Following persons participated in this
consideration: I.N.Gashenenko (Ukraine), A.A.Ilyukhin (Russia), M.P.Kharlamov
(Russia), A.M.Kovalev (Russia), T.S.Krasnopolskaya
(Ukraine), M.E.Lesina (Ukraine), V.V.Meleshko
(Ukraine), V.V.Sokolov (Russia), V.N.Tkhai
(Russia), H.M.Yehia (Egypt).
They discussed the works of D.L.Abrarov on the exact solvability of the Euler-Poisson
equations in terms of exponents of L-functions
of elliptic curves over the field of rational numbers. Their opinions can be
summarized in the following way. In his works, D.L.Abrarov
makes an attempt to give a new mathematical description of the problem. It is
necessary to interpret the obtained results in the language which is accepted
among the specialists in the given scientific area and to present the strictly
grounded facts that can be verified.
The abstract of V.N.Onikiychuk's communication was not published in the
Book of abstracts, the Organizing Committee decided to give him an opportunity
to speak at the Round Table. The participants of the conference suggested that
the author should state his results in the scientific articles for submitting to
the specialized journals, with attention to the opinion of reviewers and
authoritative scholars.
The 11th
International conference "Stability, control and rigid bodies
dynamics" is supposed to be held in the beginning of September, 2011.
Alexander M.Kovalev,
Professor, Dr. Sci. Phys. & Math., Correspondent
member of the National Academy of Sciences of Ukraine, Director of the
Institute of Applied Mathematics and Mechanics of NASU. Basic scientific
interests: mathematical control theory, rigid bodies dynamics, stability
theory. kovalev@iamm.ac.donetsk.ua
Boris I.Konosevich, Candidate of physical and
mathematical sciences, senior research worker of the Institute of Applied
Mathematics
and Mechanics of NASU. Fields of scientific interests:
dynamics of rigid bodies systems, stability of motion, exterior ballistics.
konos@iamm.ac.donetsk.ua
