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

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 $\theta(t)$ 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

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 $p = - \frac{A}{\rho}$, $A>0$. Since empty spacetime ($p = \rho = 0$) 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 $r = a$. 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.

Dilaton thin-shell wormholes supported by a generalized Chaplygin gas

In this article, we construct spherical thin-shell wormholes with charge in dilaton gravity. The exotic matter required for the construction is provided by a generalized Chaplygin gas. We study the stability under perturbations preserving the symmetry. We find that the increase of the coupling between the dilaton and the electromagnetic fields reduces the range of the parameters for which stable configurations are possible.Comment: 14 pages, 6 figures. v3: typos correcte

On a family of integrable systems on S2S^2 with a cubic integral of motion

We discuss a family of integrable systems on the sphere $S^2$ 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

Thin-shell wormholes with a generalized Chaplygin gas

In this article, spherically symmetric thin-shell wormholes supported by a generalized Chaplygin gas are constructed and their stability under perturbations preserving the symmetry is studied. Wormholes with charge and with a cosmological constant are analyzed and the results are compared with those obtained for the original Chaplygin gas, which was considered in a previous work. For some values of the parameters, one stable configuration is also present and a new extra unstable solution is found.Comment: 14 pages, 6 figures; v2: typos corrected and minor rewordin

Modified Chaplygin Traversable Wormholes

The modified Chaplygin gas (MCG) is a strong candidate for the unified model of dark matter and dark energy. The equation of state of this modified model is valid from the radiation era to the $\Lambda$CDM model. In early epoch (when $\rho$ was large), dark matter had the dominant role while at later stages (when $\rho$ is small), the MCG model behaves as dark energy. In this work, we have found exact solution of static spherically symmetric Einstein equations describing a wormhole for an inhomogeneous distribution of modified Chaplygin gas. For existence of wormhole solution, there are some restrictions relating the parameters in the equation of state for MCG and the throat radius of the wormhole. Physical properties and characteristics of these modified Chaplygin wormholes are analyzed in details.Comment: 9 pages, 1 figur

Generalized Chaplygin Gas Model: Dark Energy - Dark Matter Unification and CMBR Constraints

The generalized Chaplygin gas (GCG) model allows for an unified description of the recent accelerated expansion of the Universe and the evolution of energy density perturbations. This dark energy - dark matter unification is achieved through an exotic background fluid whose equation of state is given by $p = - A/\rho^{\alpha}$, where $A$ is a positive constant and $0 < \alpha \le 1$. Stringent constraints on the model parameters can be obtained from recent WMAP and BOOMERanG bounds on the locations of the first few peaks and troughs of the Cosmic Microwave Background Radiation (CMBR) power spectrum as well as SNe Ia data.Comment: 9 pages, 2 figures; essay selected for an honorable mention by the Gravity Research Foundation, 200

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 $\nu$ and the $\alpha$ parameters. We use different astronomical data for restricting these parameters. It is shown that the constraint $\nu \lesssim \alpha$ 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