# Mechanics

## Temperature Distribution Inside the Ring of Liquid with Two Free Borders in the Nonclassical Model of Hydrodynamics

The article deals with the task to determine the velocity field and temperature field inside the insulated ring of incompressible viscous fluid with two free boundaries in the non-classical model of hydrodynamics. The solution to the Navier – Stokes equations and heat equation obtained by numerical methods. Analysis of the results of numerical experiments reveal the effect of nondissipative viscosity on the temperature distribution inside the ring.

## Construction and Stabilization Program Motions of Nonautonomous Hamiltonian Systems

We consider program motion of Hamiltonian system and solve the problem of construction asymptotically stability programm motion. The programm motion can be any function. Control is received in the method and the method of limiting functions and systems. In this case we use the Lyapunov’s functions having constant signs derivatives. The following examples are considered: stabilization of program motions of homogeneous rod of variable length and stabilization of program motions of mathematical pendulum variable length in the rotation plane.

## Influence of the Variable Aerodynamic Moment on Satellite Attitude Motion

Attitude motion of a rigid body in the plane of a circular orbit under gravitational and aerodynamic moments is considered. The mode of the motion of a satellite gravitational stabilization when its long axis moves in the vicinity of a local vertical is investigated. Allowance of variations in the atmosphere density at a satellite orbital motion and in the aerodynamic moment coefficient depending on its orientation to an approach flow is included in the aerodynamic moment model.

## Stress of Heavy-Wall Tubing Cylindrical Pipes Taking into Account the Gravity for Materials with Difficult Rheology

Within a method of small parametre the field of stresses of heavy tubing cylindrical pipes is investigated at modelling of a material by the incompressible elasticis viscous-plastic environment. The estimation of influence on size of a plastic zone physicomechanical design parametres is given.

## Boundary Properties of Generalized Cauchy Type Integrals in the Space of Smooth Functions

The generalized Cauchy type integrals which kernel depends on the difference of arguments are considered on the smooth contour. These integrals cover as potentials of double layer for second order elliptic equations as generalized Cauchy type integrals for first order elliptic systems on the plane. In the paper the sufficient conditions such that these integrals belong C n,μ up to the boundary are found.

## Creeping Flow of Viscoelastic Fluid with Free Surface at Non-Isothermal Condition

Numerical simulation flow of viscoelastic fluid with free surface, which is realized in entrance and output flow in extrusion die was performed. The flow of liquid is described by equations of conservation of mass, momentum and thermal energy with rheological constitutive equation of Giesekesus. On basis of finite element method the stable numerical scheme was developed to solve this problem. Different numerical experiments was performed to define the configuration of outflow jet in various regimes and construction of die.

## Finite Integral Transformations Method — Generalization of Classic Procedure for Eigenvector Decomposition

The structural algorithm of the finite integral transformation method is presented as a generalization of the classical procedure of eigenvector decomposition. The initial-boundary problems described with a hyperbolic system of linear partial second order differential equations are considered. The general case of non-self adjoint solution by expansion in the vector-functions is possible only by the use of biorthogonal of finite integral transformations.

## Modeling of Polymer Fiber Evaporation

Solvent evaporation process from the surface of two-phase polymer solution axisymmetric fiber is analyzed. Fick’s law of mass diffusion was employed under the condition that the solvent diffusion depends upon the solvent concentration according to the Vrentas – Duda free-volume theory. Numerical results are provided for the PAN/DMF fibers of different initial radii that are close to jet radii in electrospinning experiments.

## The Intense State of the Band of Variable Thickness at Non-Uniform Heating

The problem of mechanics of fracture for a band (core) weakened by a rectilinear crack with end zones, a non-uniform temperature field being under action is considered. Thickness of a band is considered a variable. The condition of a limiting condition of a band is received.

## Modelling of the Longitudinal Impact Springy Rod as Mechanical System with Final Number of the Degree of the Liberty

The model of the longitudinal impact rod was designed as mechanical system with final number of the degrees of the liberty. The Equations of the motion are transformed to type, when in structure of the equations is presented parameter, defining velocity of the sound in material rod. This allows the natural image to match the results with wave model of the longitudinal impact. The Presented algorithm of the numerical decision of the equations of the motion and its realization at modeling of the longitudinal impact of the test object.