Vol 54, No 4 (2019)

The problem of optimal control of reorientation of an absolutely rigid spherically symmetric body is investigated. An integral-quadratic functional characterizing the total energy consumption was chosen as a criterion for the effectiveness of maneuver. Main moment of applied external forces serves as control. In this problem, for the first time, a family of analytic extremal trajectories is obtained, which are uniquely determined in accordance with the requirement that the absolute value of the angular velocity vector function be constant in time. Illustrative examples are provided.

Approaches that allow one to describe the elastic dynamics of a medium (including unloading and elastic loading) in the presence of irreversible pre-deformations are proposed for a model of large elastoplastic deformations. Formulas based on a rotation tensor are obtained for calculating the redistribution of plastic strains. For dynamic elastic processes generating shock waves in an elastoplastic medium, the possible rates and types of plane shock waves are determined. It is shown that elastic shock waves create jumps in the field of plastic pre-deformations. Relations for calculating such discontinuities are obtained. The main properties of modeling self-similar solutions taking into account the proposed approach to the description of the kinematics of the medium and the possibility of distinguishing between elastic and plastic strains are considered.

The results of experimental studies of the penetration of solids moving by inertia into a. medium composed of layers of plasticine of different strengths (previously held at different temperatures) are presented. A. steel ball and a. conical body were used. The dependence of the penetration depth on the thickness and relative position of the frozen and warm layers was determined, as well as the effect of the ratio of the layer thickness to the length of the streamlined body on the result.

The effect of the average excess pressure of the environment on the linear and nonlinear bending of a round plate is studied. Different values of the gas pressure on both surfaces of the plate form a transverse distributed load, consisting of a differential pressure and the interaction of the average pressure with the curvature of the middle surface. With a small ratio of the average pressure to the elastic modulus of the material and with a large relative thickness, the influence of the second component of the bending load is small. With a large ratio of the average pressure to the elastic modulus and a small relative thickness, this effect is significant.

The present study deals with the application of methods of perturbation theory, mass reduction, and strength of materials to an analytical solution of the problem on dependence of the eigenfrequencies of a real rotor on rotation speed. The obtained approximate solution is compared with the numerical one.

In the framework of the celestial-mechanical approach, a long-period forecasting model of the pole motion is developed, taking into account perturbations from the Sun and the Moon with periods of one year and 18.61 years, respectively. The refined model takes into account the dynamic effects of the spatial motion of the Earth-Moon system in the oscillatory process of the Earth’s pole. Using numerical-analytical modeling, the possibilities of identifying the parameters of the Earth’s pole oscillation and approximating the developed refined model to real trajectory measurements are considered. Estimates of the accuracy of forecasting the motion of the pole are given taking into account additional terms caused by the lunar perturbation.

The exact solutions of the Pochhammer-Cree wave equation, which describes the propagation of harmonic waves in an elastic cylindrical rod, are analyzed. For longitudinal axially symmetric modes, a spectral analysis of the matrix of the dispersion equation is carried out for the first time. Analytical expressions for wave polarization are obtained. On the surface of the rod for the fundamental longitudinal axially symmetric mode, the polarization coefficients of the corresponding waves are determined and the variation of these coefficients depending on the frequency is analyzed. It was found that at the phase velocity of the fundamental axially symmetric longitudinal mode, which coincides with the shear wave velocity, all components of displacements on the side surface of the rod simultaneously vanish, which seems to be extremely important for the design of acoustic waveguides.

It is a great challenge for the universities to present undergraduate students the fundamental knowledge needed to develop intelligent unstable robots. Due to the inherent instability and nonholonomic constraints, the problem of two-wheeled inverted pendulum (TWIP) mobile robot is appealing and challenging case in control and dynamic systems. In this paper, an approach is presented to introduce undergraduate students of the control engineering, the principle of developing a. TWIP mobile robot. For this purpose, a. conceptual design algorithm for TWIP robots is contributed and based on the algorithm and the design criteria, a. prototype of the robot is constructed. In the construction process, the selection of mechanical and electronic components is based on the algorithm and the students can experience different control techniques to stabilize and control the system.