Rotational-oscillational motions of the nonrigid Earth about the center of mass

We use the model of a nearly axisymmetric viscoelastic rigid body to study perturbed rotational-oscillational motions of the Earth’s pole. We point out that the Chandler component of oscillations is of celestial-mechanics nature and is caused by the gravitational-tidal actions of the Sun and the Moon. We analyze the pole oscillation excitation mechanism at a frequency close to the Chandler frequency and show that the undamped pole oscillations are caused by the resonance harmonic of the external perturbation at a frequency close to the free nutation frequency. We discuss whether it is possible to solve the problem of constructing a short-term forecast of the pole motion on the basis of a polynomial filter obtained by the least-squares method without taking into account small-scale oscillations caused by wide-band random factors of arbitrary physical nature. In the present paper, we perform numerical simulation of tidal inhomogeneities in the Earth’s axial rotation. Attention is mainly paid to the analysis of day length variations on short time intervals with periods less than or equal to one year (interannual oscillations) and to their forecast.     

Three-dimensional magnetohydrodynamic description of the process of impingement of a solar wind rotational discontinuity on the Earth’s bow shock

The impact of the plane front of a rotational discontinuity, which has a circular polarization and propagates in the solar wind along the Sun-Earth radius, on the Earth’s bow shock and the magnetosheath is first investigated in the three-dimensional formulation. The most characteristic values of the solar wind parameters and the interplanetary magnetic field strength in the Earth’s orbit are considered. The global three-dimensional pattern of the flow is constructed as a function of the latitude and longitude of points on the bow shock and the intensities of all the waves appearing in the interaction which significantly depend on the angle of rotation of the magnetic field are found. The solution obtained is necessary to interpret the solar wind parameters and the interplanetary magnetic field measured by spacecraft located in the neighborhood of the Lagrange point and the Earth’s magnetosphere.     

Vertical Momentum Transfer Induced by Internal Inertial-Gravity Waves in Flow with Account of Turbulent Viscosity and Diffusion

Fluid Dynamics - Free internal waves in a two-dimensional vertically inhomogeneous stratified flow are considered in the Boussinesq approximation with account of the Earth’s rotation and...     

Adaptive filtering of airborne gravimetry data using hidden Markov models

The adaptive filtering of airborne gravimetry data on the flight path of an aircraft is discussed with consideration of the nonuniformity of the Earth’s gravity field due to the inhomogeneity of the Earth’s crust, topography, etc. Nonuniformity is described by a hidden Markov model with a finite number of states; each state corresponds to a certain type of the gravity anomaly profile. The problem under study is solved with consideration of GPS errors.     

Problems of folding in the earth’s stratified crust

The problem of folding in the Earth’s stratified crust is addressed within the framework of solid mechanics. The history and formulation of the problem and approaches to its solution are briefly outlined. The initial stage of folding in strata with different mechanical properties is studied in detail using the piecewise-homogeneous medium model and the three-dimensional theory of stability. Conclusions of applied and fundamental importance are drawn from an analysis of solutions to a wide range of specific problems __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 2, pp. 3–44, February 2007.     

Fluctuations of pole oscillations of deformable earth under nonstationary perturbations

An approach of celestial mechanics is used to consider variations in the tensor of inertia due to elastic deformations arising under the action of the centrifugal potential. The effects of influence of random actions are investigated in an example of fluctuation-dissipative perturbations of geophysical nature. A combined model of the Earth rotation fluctuations permits taking into account the stochastic components of the pole tide. It is shown that small irregular perturbations in tidal processes generate variations in the Chandler component of the pole oscillations.     

Determining the temperature on the sides of a microsatellite

An approach to determine the temperature on the sides of a satellite is proposed depending on the thermal coefficients of absorption and emissivity as well as on the altitude and inclination of the satellite orbit. The shape of the satellite, the solar heat radiation, the Earth’s heat radiation, and the Earth’s albedo are considered among the other factors affecting the satellite.     

A molecular mechanics approach for analyzing tensile nonlinear deformation behavior of single-walled carbon nanotubes

In this paper, by capturing the atomic information and reflecting the behaviour governed by the nonlinear potential function, an analytical molecular mechanics approach is proposed. A constitutive relation for single-walled carbon nanotubes (SWCNT’s) is established to describe the nonlinear stress-strain curve of SWCNT’s and to predict both the elastic properties and breaking strain of SWCNT’s during tensile deformation. An analysis based on the virtual internal bond (VIB) model proposed by P. Zhang et al. is also presented for comparison. The results indicate that the proposed molecular mechanics approach is indeed an acceptable analytical method for analyzing the mechanical behavior of SWCNT’s. The project supported by the National Natural Science Foundation of China (10121202, 90305015 and 10328203), the Key Grant Project of Chinese Ministry of Education (0306) and the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU 7195/04E).     

Effect of physical and chemical nonequilibrium processes on the parameters of the near wake downstream of a spacecraft

The axisymmetric laminar flowfield and heat transfer characteristics of the RAM-C experimental spacecraft moving in the Earth’s atmosphere at an altitude of 61 km and a velocity of 7.65 km/s are investigated on the basis of a numerical solution of the Navier-Stokes equations. In studying the effect of the physical and chemical nonequilibrium processes on the flow parameters two approximations are employed for describing the gas properties, namely, that of a perfect gas with a constant adiabatic exponent and a model of dissociating and vibrationally-relaxing air. Emphasis is placed on the study of the spacecraft’s near-wake parameters. The results obtained are compared with experimental data on the electron concentration in the shock layer on the lateral surface and the calculated results of other authors.     

Three-dimensional magnetohydrodynamic description of the process of collision of a solar wind shock wave and the Earth’s bow shock

The propagation of a solar wind shock wave along the surface of the Earth’s bow shock is investigated within the framework of an ideal magnetohydrodynamic model in the three-dimensional non-plane-polarized formulation. The most characteristic values of the solar wind parameters and the interplanetary magnetic field strength are considered for the plane front of a solar wind shock wave moving at various velocities along the Sun-Earth radius. The global three-dimensional pattern of the interaction is constructed as a function of the angle of inclination of the surface of the bow shock to the solar wind velocity and the azimuthal angle along the curve of intersection of the fronts of the interacting shock waves. The evolution of the flow developed in the neighborhood of the bow shock is investigated and the parameters of the medium and magnetic field are calculated.     

On the formation of linear folds in regularly layered rock masses under biaxial loading

The piecewise-homogeneous model and the three-dimensional theory of stability for small and finite subcritical strains are used to study the formation of folds in layered rock masses of the Earth’s crust under biaxial loading. The general statement of the problem is given, and the governing characteristic equations are derived. Numerical results are presented for a layered rock mass composed of two alternating layers __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 26–34, December 2005.     

Dependence of the height of disappearance for small meteoric bodies on their parameters

A new method for determining the parameters of small meteoric bodies by the height of disappearance on entering the Earth’s atmosphere is proposed. The heat transfer processes in front of a body are taken into account. Some numerical results for a number of small meteoric bodies observed by the Canadian camera network are discussed.     

Quasi-Periodic Attractors in Celestial Mechanics

We prove that KAM tori smoothly bifurcate into quasi-periodic attractors in dissipative mechanical models, provided external parameters are tuned with the frequency of the motion. An application to the dissipative spin–orbit model of celestial mechanics (which actually motivated the analysis in this paper) is presented.     

On a formulation of meteor physics problems

The general equation describing the motion of a meteoroid in the Earth’s atmosphere is considered. It is shown that, in this case, the momentum variation of the system consisting of the meteoroid and its separating mass is due to the velocity variation of the meteoroid. The projection of Newton’s equation onto the tangent to the meteoroid trajectory is analyzed. It is also shown that, because of large geocentric velocities (between 11 and 72 km/s), the dominant force is the drag force proportional to the square of the incident air flow velocity. Some numerical results obtained for the Bene>sov bolide registered by the European Fireball Network (May 7, 1991) are given as an illustrative example.     

Transient heat conduction from a vertical rod buried in a semi-infinite medium with variable heating strength

In this paper, a variable heating strength model (VHS model) is developed to predict transient heat conduction from a vertical rod buried in a semi-infinite medium. Unlike past studies, the current VHS model permits a VHS along the rod. Both axial heat conduction through the rod and lateral heat conduction to the surrounding ground are modeled. A derived distribution of axial heating strength is then applied to a finite line heat source model to predict transient temperature changes in the surrounding medium. The predicted results show how the rod’s radius and ground’s thermal conductivity affect the vertical variation of heating strength and temperature response. Additional simulations predict the long-term temperature increase in the ground, due to a power transmission tower installed in a region of initially frozen ground.     

Academician Nikolai Nikolaevich Bogolyubov (for the 100th anniversary of his birth)

This paper is dedicated to the memory of N. N. Bogolyubov in recognition of his towering stature in nonlinear mechanics and theoretical physics, his remarkable many-sided genius, and the originality and depth of his contribution to the world’s science. The paper briefly describes Bogolyubov’s achievements in nonlinear mechanics, classical statistical physics, theory of superconductivity, quantum field theory, and strong interaction theory     

A Variational Approach to the Macroscopic Electrodynamics of Anisotropic Hard Superconductors

We consider Bean’s critical state model for anisotropic superconductors. A variational problem solved by the quasi-static evolution of the internal magnetic field is obtained as the Γ-limit of functionals arising from Maxwell’s equations combined with a power law for the dissipation. Moreover, the quasi-static approximation of the internal electric field is recovered, using a first order necessary condition. If the sample is a long cylinder subjected to an axial uniform external field, the macroscopic electrodynamics is explicitly determined.     

A historical perspective of Menabrea’s theorem in elasticity

This paper presents the theorem proposed by Luigi Federico Menabrea to study linear elastic redundant systems. Some of Menabrea’s papers on the subject are examined, as well as the criticism and the corrections brought to his first proof. We consider Menabrea’s work in the frame of the studies of his contemporaries; we try to provide a historical and epistemological background for Menabrea’s theorem and for its consequences in modern mechanics.     

Fluid convection in a rotating porous layer under modulated temperature on the boundaries

The linear stability of thermal convection in a rotating horizontal layer of fluid-saturated porous medium, confined between two rigid boundaries, is studied for temperature modulation, using Brinkman’s model. In addition to a steady temperature difference between the walls of the porous layer, a time-dependent periodic perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. The combined effect of rotation, permeability and modulation of walls’ temperature on the stability of flow through porous medium has been investigated using Galerkin method and Floquet theory. The critical Rayleigh number is calculated as function of amplitude and frequency of modulation, Taylor number, porous parameter and Prandtl number. It is found that both, rotation and permeability are having stabilizing influence on the onset of thermal instability. Further it is also found that it is possible to advance or delay the onset of convection by proper tuning of the frequency of modulation of the walls’ temperature.     

Dissipation-induced instabilities and symmetry

The paradox of destabilization of a conservative or non-conservative system by small dissipation,or Ziegler’s paradox(1952),has stimulated a growing interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations.Since the last decade it has been widely accepted that dissipation-induced instabilities are closely related to singularities arising on the stability boundary,associated with Whitney’s umbrella.The first explanation of Ziegler’s paradox was given(much earlier)by Oene Bottema in 1956.The aspects of the mechanics and geometry of dissipation-induced instabilities with an application to rotor dynamics are discussed.