226 research outputs found
On the motion of a heavy rigid body in an ideal fluid with circulation
Chaplygin's equations describing the planar motion of a rigid body in an
unbounded volume of an ideal fluid involved in a circular flow around the body
are considered. Hamiltonian structures, new integrable cases, and partial
solutions are revealed, and their stability is examined. The problems of
non-integrability of the equations of motion because of a chaotic behavior of
the system are discussed.Comment: 25 pages, 4 figure
On a family of integrable systems on with a cubic integral of motion
We discuss a family of integrable systems on the sphere with an
additional integral of third order in momenta. This family contains the
Coryachev-Chaplygin top, the Goryachev system, the system recently discovered
by Dullin and Matveev and two new integrable systems. On the non-physical
sphere with zero radius all these systems are isomorphic to each other.Comment: LaTeX, 8 page
Some new class of Chaplygin Wormholes
Some new class of Chaplygin wormholes are investigated in the framework of a
Chaplygin gas with equation of state , . Since
empty spacetime () does not follow Chaplygin gas, so the
interior Chaplygin wormhole solutions will never asymptotically flat. For this
reason, we have to match our interior wormhole solution with an exterior vacuum
solution i.e. Schwarzschild solution at some junction interface, say .
We also discuss the total amount of matter characterized by Chaplygin gas that
supplies fuel to construct a wormhole.Comment: 14 pages, 12 figures, Accepted for publication in Mod.Phys.Lett.
Dynamics of a rolling robot
Equations describing the rolling of a spherical ball on a horizontal surface are obtained, the motion being activated by an internal rotor driven by a battery mechanism. The rotor is modeled as a point mass mounted inside a spherical shell and caused to move in a prescribed circular orbit relative to the shell. The system is described in terms of four independent dimensionless parameters. The equations governing the angular momentum of the ball relative to the point of contact with the plane constitute a six-dimensional, nonholonomic, nonautonomous dynamical system with cubic nonlinearity. This system is decoupled from a subsidiary system that describes the trajectories of the center of the ball. Numerical integration of these equations for prescribed values of the parameters and initial conditions reveals a tendency toward chaotic behavior as the radius of the circular orbit of the point mass increases (other parameters being held constant). It is further shown that there is a range of values of the initial angular velocity of the shell for which chaotic trajectories are realized while contact between the shell and the plane is maintained. The predicted behavior has been observed in our experiments
On integrable system on with the second integral quartic in the momenta
We consider integrable system on the sphere with an additional integral
of fourth order in the momenta. At the special values of parameters this system
coincides with the Kowalevski-Goryachev-Chaplygin system.Comment: LaTeX, 6 page
Dynamics of the Tippe Top -- properties of numerical solutions versus the dynamical equations
We study the relationship between numerical solutions for inverting Tippe Top
and the structure of the dynamical equations. The numerical solutions confirm
oscillatory behaviour of the inclination angle for the symmetry
axis of the Tippe Top. They also reveal further fine features of the dynamics
of inverting solutions defining the time of inversion. These features are
partially understood on the basis of the underlying dynamical equations
Integrable Euler top and nonholonomic Chaplygin ball
We discuss the Poisson structures, Lax matrices, -matrices, bi-hamiltonian
structures, the variables of separation and other attributes of the modern
theory of dynamical systems in application to the integrable Euler top and to
the nonholonomic Chaplygin ball.Comment: 25 pages, LaTeX with AMS fonts, final versio
РАСЧЁТ ПОЛЕЙ И ТОКОВ В ИНДУКТОРНОЙ СИСТЕМЕ С ПРИТЯГИВАЮЩИМ ЭКРАНОМ И ДОПОЛНИТЕЛЬНЫМ ВИТКОМ КАК ИНСТРУМЕНТА РИХТОВКИ
In the idealization of the "limiting low" frequencies of acting fields the calculated dependences for the density of the induced currents and distributed force of the attractive in the induction system with attractive screen and the external additional coil which allow to evaluate the characteristics of flowing electrodynamics processes and make recommendations for the design of the real tools for magnetic-pulse attractive of nonmagnetic thin-walled sheet metals are obtained.В идеализации "предельно низких" частот действующих полей получены расчётные зависимости для плотности индуцированных токов и распределенной силы притяжения в индукторной системе с притягивающим экраном и внешним дополнительным витком, позволяющие провести оценки характеристик протекающих электродинамических процессов и дать рекомендации по проектированию реальных инструментов для магнитно-импульсного притяжения немагнитных тонкостенных листовых металлов.В ідеалізації "гранично низьких" частот діючих полів отримані розрахункові залежності для щільності індукованих струмів і розподіленої сили тяжіння в індукторній системі з притягуючим екраном і зовнішнім додатковим витком, що дозволяють провести оцінки характеристик протікаючих електродинамічних процесів і дати рекомендації з проектування реальних інструментів для магнітно-імпульсного притягування немагнітних тонкостінних листових металів
Observational Constraints on the Generalized Chaplygin Gas
In this paper we study a quintessence cosmological model in which the dark
energy component is considered to be the Generalized Chaplygin Gas and the
curvature of the three-geometry is taken into account. Two parameters
characterize this sort of fluid, the and the parameters. We use
different astronomical data for restricting these parameters. It is shown that
the constraint agrees enough well with the astronomical
observations.Comment: Accepted by IJMPD; 18 pages; 10 Figure
ЭКСПЕРИМЕНТАЛЬНЫЕ ИССЛЕДОВАНИЯ РАСПРЕДЕЛЕНИЯ ТОКА НА ПОВЕРХНОСТИ ЛИСТОВОЙ ЗАГОТОВКИ В ЛИНЕЙНЫХ ИНСТРУМЕНТАХ МАГНИТНО-ИМПУЛЬСНОГО ПРИТЯЖЕНИЯ
Purpose. The purpose of the present work consists in the characteristics experimental determination of the pulsed current transverse distribution on the surface of a sheet non-magnetic metal between the point contacts of the power source with different geometry of their connection under operating frequencies variation. Methodology. The measurements were carried out using methods based on the known positions of electromagnetism. The simulating low-voltage equipment was used, as well as high-voltage power sources with a high level of the stored energy. Numerical processing of the measurement results was carried out using standard programs from the «Wolfram Mathematica» package. Results. The space-temporal shapes of the pulsed current density transverse distribution on the surface of the sheet blank were obtained and analyzed. It is established that the degree of transverse current concentration in sheet metal relative to the center of the system in the operating frequency range of ~ 1.8…22 kHz depends very little on its temporal characteristics. It was found that the level of the transverse current concentration in the conditionally allocated band connecting the contacts of connection depends significantly on the ratio of the width of this band and the transverse dimensions of the contact connection. Moreover, the smallest current is concentrated in a strip whose width is much less than the distance between the contacts (£ 11…16 %). Originality. For the first time, the numerical estimates degree of the current transverse concentration are obtained and the dependence of this parameter on the temporal characteristics of the current, as well as on the method of connecting the power source contacts, is established. Practical value. The research results will allow creating the new more efficient linear tools of magnetic-pulsed attraction of sheet metals, based on the force interaction of conductors with unidirectional currents. Целью работы является экспериментальное определение характеристик поперечного распределения плотности импульсных токов разной частоты на поверхности листового немагнитного металла между точечными контактами источника мощности при различной геометрии их подключения. Методика. Измерения проводились с помощью методов, основанных на известных положениях электромагнетизма. Использовалось модельное низковольтное оборудование, а также высоковольтные источники мощности с высоким уровнем запасаемой энергии. Численная обработка результатов измерений проводилась с помощью стандартных программ из пакета «Wolfram Mathematica». Результаты. Получены и проанализированы пространственно-временные формы поперечного распределения плотности импульсного тока на поверхности листовой заготовки. Научная новизна. Впервые получены численные оценки степени поперечной концентрации тока и установлена зависимость данного параметра от временных характеристик тока, а также от способа подключения контактов источника мощности. Практическое значение. Результаты исследований позволяют создавать новые более эффективные линейные инструменты магнитно-импульсного притяжения листовых металлов, основанные на силовом взаимодействии проводников с однонаправленными токами
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