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Об устойчивости и ветвлении стационарных вращений в плоской задаче о движении взаимно гравитирующих треугольника и материальной точки
Нелинейная динамика. 2016. Т. 12. № 2. С. 179-196.
Burov A. A., Nikonov V.
The planar motion of an equilateral triangle with equal masses at vertices and of a point subjected to mutual Newtonian attraction is considered. Necessary conditions for the stability of “straight”, axial steady configurations, when the massive point is located on one of the symmetry axes of the triangle, are studied. The generation of other, “oblique”, steady configurations is discussed in connection with the variation, for certain parameter values, of the degree of instability of some “straight” steady configurations.
Priority areas:
mathematics
Language:
Russian
Burov A. A., Герман А. Д., Косенко И. И. et al., Нелинейная динамика 2017 Т. 2013 № 2 С. 243-256
The problem of the motion of a particle in the gravity field of a homogeneous dumbbell-like
body composed of a pair of intersecting balls, whose radii are, in general, different, is studied.
Approximation for the Newtonian potential of attraction is obtained. Relative equilibria and
their properties are studied under the assumption of uniform rotation of the dumbbells. ...
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В сборник трудов включены доклады ХХI-го Международного симпозиума «Надежность и качество», проходившего с 23 по 29 мая 2016 г. в городе Пензе.
Рассмотрены актуальные проблемы теории и практики повышения надежности и качества; эффективности внедрения инновационных и информационных технологий в фундаментальных научных и прикладных исследованиях, образовательных и коммуникативных системах и средах, экономике и юриспруденции; методов и средств ...
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A.A. Burov, Kosenko I. I., Journal of Applied Mathematics and Mechanics 2014 Vol. 78 No. 6 P. 587-598
The Lagrange equations are considered in the case when the Lagrangen function is independent of some of the velocities, and the properties of the differential-algebraic equations arising are studied. It is proved that, when non-degeneracy conditions are satisfied, the equations arising reduce to differential Lagrange equations of lower dimension. The problem of the planar oscillations ...
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Burov A. A., Герман А. Д., Распопова Е. А. et al., Нелинейная динамика 2018 Т. 14 № 1 С. 45-52
It is well known that several small celestial objects are of irregular shape. In particular, there exist asteroids of the so-called “dog-bone” shape. It turns out that approximation of these bodies by dumb-bells, as proposed by V.V. Beletsky, provides an effective tool for analytical investigation of dynamics in vicinities of such bodies. There remains the ...
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Alexander A.Burov, Guerman A., Kosenko I., Acta Astronautica 2015 Vol. 116 No. November–December P. 349-354
We consider the problem of in-plane rotations of a space elevator with variable tether length attached to a surface of one of the primaries in a double system. The planet and its moon (or two asteroids) move about their center of mass in unperturbed elliptic Keplerian orbits. We discuss the possibilities to cause a prescribed ...
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Burov A. A., Kosenko I. I., Mechanics of Solids 2014 Vol. 49 No. 5 P. 506-517
In the usual everyday life, it is well known that the inverted pendulum is unstable and is ready to fall to “all four sides,” to the left and to the right, forward and backward. The theoretical studies and the lunar experience of moon robots and astronauts also confirms this property. The question arises: Is this ...
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Burov A.A., German A. D., Kosenko I. I., Cosmic Research (USA) 2014 Vol. 52 No. 4 P. 289-294
The problem of planar oscillations of a pendulum with variable length suspended on the Moon’s surface is considered. It is assumed that the Earth and Moon (or, in the general case, a planet and its satellite, or an asteroid and a spacecraft) revolve around the common center of mass in unperturbed elliptical Keplerian orbits. We ...
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Каз. : СМУиС, 2013
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Буров А.А., Герман А. Д., Косенко И. И., Космические исследования 2014 Т. 52 № 4 С. 307-312
The problem of planar oscillations of a pendulum with variable length suspended on the Moon’s surface is considered. It is assumed that the Earth and Moon (or, in the general case, a planet and its satellite, or an asteroid and a spacecraft) revolve around the common center of mass in unperturbed elliptical Keplerian orbits. We ...
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В трудах нашли отражение вопросы технологической механики и механики деформируемого твердого тела, аэродинамики, тепломассообмена, математического моделирования, управления полетом летательных аппаратов, автоматизированного проэктирования и управления процессами разработки и производства летательных аппаратов и двигательных установок авиационной и космической техники.Опубликованные материалы соответствуют перечню Критических технологий Российской Федерации, утвержденному президентом РФ (технологии создания и управления новыми видами транспортных систем; ...
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Пенза : ПГУ, 2015
В сборник трудов включены доклады юбилейного ХХ-го Международного симпозиума «Надежность и качество», проходившего с 25 по 31 мая 2015 г. в городе Пензе.
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Balandin D., Nikonov V., Вестник Московского университета. Серия 1: Математика. Механика 2016 Vol. 71 No. 3 P. 51-57
Similarities and differences between the force fields of a classical real dipole and a complex dipole are analyzed. The complex dipole is a pair of points equipped with complex conjugate masses and situated in a complex domain. The results of this analysis are used in the problem of motion of a material point in the ...
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Burov A.A., Guerman A. D., Kosenko I. I., Celestial Mechanics and Dynamical Astronomy 2014 Vol. 120 No. 3 P. 337-347
This study focuses on spatial motion of the lunar elevator which is studied in the framework of elliptical restricted three-body problem. Analysis of dynamics of a spacecraft anchored to the Moon by a tether is done assuming that the tether’s length can be changed according to a prescribed law. The goal is to find the ...
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Зайцев В. И., Щавелин В. М., / Московский инженерно-физический институт. Серия 001-86 "Препринт МИФИ". 1986. № 001-86.
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Aksenov S. A., Bober S. A., Guskova M., Advances in Space Research 2021 Vol. 68 No. 6 P. 2501-2514
In the framework of circular restricted three-body problem the libration point orbits form the families of periodic and quasi-periodic solutions. In the paper, the mapping of initial conditions is utilized to describe and study the structure and properties of these families. A new numerical method for orbit generation, which is applicable both for the periodic ...
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M. : Association of graduates and employees of AFEA named after prof. Zhukovsky, 2018
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Издательство Казанского (Приволжского) федерального университета, 2016
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Burov A. A., Yakushev I. A., Journal of Applied Mathematics and Mechanics 2014 Vol. 78 No. 5 P. 460-467
The sliding of a heavy bead, threaded on a thin circular hoop, rotating with a constant angular velocity around a vertical axis, situated in its plane and, in the general case, not passing through its vertical diameter, is considered. It is assumed that dry friction acts between the bead and the hoop. A set of ...
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Зайцев В. И., Щавелин В. М., М. : ВИНИТИ РАН, 1985
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Burov A. A., Shalimova E. S., Regular and Chaotic Dynamics 2015 Vol. 20 No. 3 P. 225-233
The problem of motion of a heavy particle on a sphere uniformly rotating about a fixed axis is considered in the case of dry friction. It is assumed that the angle of inclination of the rotation axis is constant. The existence of equilibria in an absolute coordinate system and their linear stability are discussed. The ...
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