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

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