# Mechanics

## Determination of elastic characteristics of polymeric covers by results of tests of flat specimens at tension and bending

The results of experimental identification of elastic modulus and Poisson's ratio of thin polymeric covers on the surface of the flat specimens of steel 08-OP are presented. The values of elastic modulus were determined with the rule of the mixtures by the standard tests of the specimens with the covers at the tension and four-point bending. The values of the Poisson's ratio were obtained on the base of the comparison of the tests results and the computer modeling of the bending process the studied specimens.

## Thermomechanical orthogonality in nonlinear type-III thermoelasticity (GNIII)

The present paper is devoted to formulations of constitutive equations for the non-linear Green–Naghdi type-III thermoelastic continuum consistent with the principle of thermodynamic (or thermomechanical) orthogonality.

## About a problem of spacecraft's orbit optimal reorientation

The problem of optimal reorientation of the spacecraft's orbit is solved with the help of the Pontryagin maximum principle and quaternion equations. Control (thrust vector, orthogonal to the orbital plane) is limited in magnitude. Functional, which determines a quality of control process is weighted sum of time and module (or square) of control. We have formulated a differential boundary problems of reorientation of spacecraft's orbit.

## Research of consequences of tether's jamming in the task of payload delivery from an orbit

In article the off-normal situation of tether's jamming at the decision of the task of payload delivery from an orbit by means of a tether is considered. The mathematical model described the space tether system consisting of the basic space vehicle, the tether and the payload is used. At creation of model the mass and damping properties of the tether weren't considered. It is supposed that basic space vehicle moves on a circle orbit.

## Моделирование трещинообразования в полосе переменной толщины

Проведено математическое описание модели зарождения трещины в полосе переменной толщины. Определение неизвестных параметров, характеризующих зародышевую трещину, сводится к решению системы сингулярных интегральных уравнений. Получено условие, определяющее критическое значение внешней нагрузки, при которой происходит трещинообразование.

## Upper and low bounds of azimuthal numbers related to elementary wave functions of an elliptic cylinder

Numerical and analytical aspects of generating 2π-periodic solutions of the angular Mathieu equation obtained for the circumferential harmonics of an elliptic cylinder and localization problem for the Mathieu eigenvalues and corresponding azimuthal numbers are considred. Those are required in usual procedure of constructing the elliptic cylinder elementary wave functions playing a very important role in mathematical physics.

## Biomechanical Assessment of the Bone Ingrowth Effect During Cementless Endoprosthesis Osteointegration

Finite elementmodel of porous titaniuminserts for cementless endoprosthesis was reconstructed usingX-ray tomography. The stress distribution is calculated for a model with open-cell foam and composite bone / titanium. The results explain the mechanism of the porous structure destruction and positive influence of the osteointegration effect on the strength properties. Numerical calculations are confirmed by experimental data of the porous samples during compression testing.

## Dual Matrix and Biquaternion Methods of Solving Direct and Inverse Kinematics Problems of Manipulators, for Example Stanford Robot Arm. I

The methology of solving the direct kinematics problem of manipulators by using screw mechanics methods (dual direction cosine matrices, Clifford biquaternions) is shown on the example of Stanford robot arm. Kinematic equations of motion of the manipulator are found. These equations will be used for solving the inverce kinematics problem with the help of biquaternion theory of kinematic control.

## Configuration Space in Second Boundary Value Problem of Non-classical Plate Theory

The article contains investigation of second boundary value problem for equilibrium equation «in mixed formulation» describing nonclassical mathematical model for hinged isotropic and uniform plate under generalized Timoshenko hypothesis taking into account initial irregularities. For this problem for the first time were proved the existance of generalized solution and weak compactness of the set of approximate solutions obtained with Bubnov–Galerkin method using V. Z. Vlasov scheme.

## Dynamical Simple Edge Effect in the Cylindrical Shell with the Edge of Arbitrary Form

The purpose of the article is to generalize the results derived in the cases of a circular shell and of a shell with a cut edge. Non-stationary wave process in a cylindrical shell with an arbitrary edge is considered. Half-geodesic frame is introduced on the middle surface of the shell and dynamical simple edge effect is studied. To find the solution Laplace transform is used while the inverse transform is realized via saddle-point method.