Moscow University Mechanics Bulletin最新文献

The Poincaré–Steklov operator that maps normal stresses tonormal displacements on a part of a half-plane boundary isstudied. A boundary value problem is formulated to introduce theassociated Poincaré–Steklov operator. An integralrepresentation based on the solution to the Flamant problem foran elastic half-plane subjected to a concentrated normal force isgiven for the operator under consideration. It is found that theproperties of the Poincaré–Steklov operator depend on thechoice of kinematic conditions specifying the rigid-bodydisplacements of the half-plane. Positive definiteness conditionsof the Poincaré–Steklov operator are obtained. It is shown thata suitable scaling of the computational domain can be used toprovide the positive definiteness of this operator.

A second-order differential equation with periodic coefficients is considered. The reduction of this equation to a first-order nonlinear equation is shown. The fourth approximation of the second resonance zone and the third approximation of the third resonance zone are constructed for the Mathieu equation describing the behavior of solutions near the boundaries of these zones.

The article is devoted to deriving reference models for the problem of initial alignment of a strapdown inertial navigation system (INS) on a swing base. It is assumed that the system does not move relative to the Earth, but its body can make uncontrolled angular motions. The described models are based on the approximation of the readings of INS accelerometers from projections on the axes of the instrument reference frame ‘‘frozen’’ in the inertial space, and the orientation of the frame is determined by its position at the start of the alignment.

The stationary motions of an inhomogeneous dynamically symmetric ball on an absolutely rough plane are studied in the special case of the center of mass passing the highest point. The system is analyzed numerically, and the existence of stable and unstable precessions is discovered. The results are presented in the form of bifurcation diagrams.

The Staude cone is considered in the problem of motion of a homogeneous isosceles tetrahedron in a central Newtonian force field. The nature of the Staude cone degeneracy is studied for the case when an isosceles tetrahedron is close to regular. It is shown how the Staude cone equations can be obtained within the framework of the Routh theory.

This work proposes a mathematical model of dispersed systems with constant number densities of the dispersed and carrier phases (incompressible dispersed system). This model makes it possible to construct a physically meaningful and mathematically correct theory of the movement of bubbles in a boiling (fluidized) layer.

The flow of a film of a viscous liquid is considered. The liquid is a weak solution containing a gas phase and a volatile surfactant. The distribution of the latter in the layer is controlled by the diffusion in the liquid volume, the adsorption–desorption processes between the liquid volume and the adsorbed near-surface layer, and the evaporation from the surface into the boundary gaseous medium. The process of the gas phase penetration from the external gas flow is specified by the diffusion inside the film.

The article shows the possibility of solving the problem of the transition between periodic and point attractors in the bistable Rosenzweig–MacArthur model with modifications for the dynamics of root hemiparasitic plants and their hosts.

One-dimensional radiative-convective models are widely used for studying long-term climate and the influence of various processes (condensation of water vapor, motion of droplets, and their impacts on radiative fluxes, etc.) on the hydrodynamics of the atmosphere. However, long-term prediction of climate is difficult due to the properties of the systems of equations, i.e., a small short-wave perturbation of the basic solution leads to a local sharp increase in the amplitude of perturbation. In this work, a one-dimensional nonstationary model with quasi-hydrostatic approximation is established and the short-wave instability is analyzed for various approximate models with the quasi-hydrostatic approximation.

An inhomogeneous wave equation with dissipation in the presence of an external uncertain perturbation is considered. The problem of finding solutions with the maximum possible amplitudes is investigated. A method for solving this problem based on the Fourier method of separating variables and the Bulgakov problem of the maximum deviation of solutions of second-order ordinary differential equations with external uncertain perturbations is proposed. The application of the Fourier method is justified. The robust stability property of the considered wave equation is investigated.