# Mechanics

## Calculating of the Fastest Spacecraft Flights between Circular Orbits

The problem of optimal reorientation of spacecraft orbit is considered in quaternion formulation. Control (jet thrust vector orthogonal to the plane of the orbit) is limited in magnitude. It is necessary to minimize the duration of the process of reorientation of the spacecraft orbit. To describe the motion of the spacecraft center of mass quaternion differential equations of the orientation of the orbital coordinate system was used.

## An Asymptotic Model for the Far-Field of Rayleigh Wave in Multilayered Plate

An asymptotic model is proposed, which allows to calculate farfield of Rayleigh wave in an infinite multilayered plate subjected to non-stationary surface load. The model is derived by using of the standard asymptotic techniques. As a result, a system of two onedimensional integro-differential equations (head system) is obtained, which describes the propagation of Rayleigh waves along the plate surfaces. For the decaying wave fields in layers the boundary problems for elliptic equations are obtained.

## Propagation and Reflection of Harmonic Waves in a Plane Acoustic Layer with Non-Homogeneous Flexible Walls

A plane acoustic layer bounded by elastic membranes, one of which has an insert with different material properties, is considered. The propagation and reflection of harmonic waves in such a layer is studied. The source of vibrations is an incident mode, coming from infinity. The solution in three regions (before the insert, under the insert, after the insert) is sought as modal expansion. The numerical results for the reflected power coefficient are presented.

## Scheme Models Development of Integro-Differential Equations Numeral Calculation of Processes Dynamics in Electric Circuits

Scheme models of numeral calculation of integral-differential equations, describing transients in electric circuits are developed. It is shown that offered modeling has the best fast-acting concerning to the known calculations.

## Cross-Coupled Type-III Thermoelastic Waves of a Given Azimuthal Number in a Waveguide under Sidewall Heat Interchanging

The paper is devoted to a study of cross-coupled type-III generalized thermoelastic waves of a given azimuthal order propagating via a long cylindrical waveguide with circular cross-section. Sidewall of the waveguide is assumed free from tractions and permeable to heat. The study is carried out in the framework of coupled generalized theory of type-III thermoelasticity (GNIII) consistent with the fundamental principles of continuum thermomechanics. The type-III theory combines the both possible mechanisms of heat transfer: thermodiffusion and wave.

## Method of Boundary States as an Effective Technique of Solving of Heterogeneous Problems of Elasticity Theory

Method of boundary states in combination with perturbation technique discovers its efficiency on heterogeneous problems of elastostatics. Solutions of problems for body of geometric configuration «peg», produced from heterogeneous material with axisymmetric heterogeneity is performed and illustrated.

## Application of Program Complex ANSYS to Calculation of the Thick-Walled Pipeline Which is Exposed to High-Temperature Local Hydrogen Corrosion

The way of application of program complex ANSYS to the decision of problems of calculation of the is intense-deformed condition and destruction of the cylindrical constructive element which is in conditions of non-uniform hydrogen corrosion is considered.

## The Second Boundary Problem for the System Hyperbolic Type Second Order for Large T

In the paper we consider the control problem for objects which vibration are described by the system of ware equations with boundary condition of the second kind.

## Investigation of Quasi-Static Bending of the Bar on the Basis of Variation Problem

The investigation of the existence of quasi-static behavior of elastic cantilever bar subjected to potential external effects. For the case when the mathematical model is a variational problem is obtained statically singular point, when crossing the path of loading is a change of type of quasi-static process.

## Stability of the Cylindrical Cover with the Elastic-Viscous-Plastic Filler at Axial Compression

Within the limits of the exact three-dimensional equations of stability of an equilibrium state of a cylindrical cover with a filler is investigated at axial compression. Calculations were spent for a case when the cover material was modelled by an elastic body, and a filler material – environment with difficult rheological properties – elasticviscous-plastic. The estimation of influence on size of critical pressure of parameters of a cover and a filler is given.