mathematical simulation
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This research paper is intended to refine the aerodynamic moment of the missile based on an analysis of flight tests and results of gas dynamics software computations. The paper compares mathematical simulation results with flight test data in order to demonstrate an improved convergence due to the proposed refinement.

The simulation results of 4 kW induction motor electric drive with scalar control system and different control topologies are presented. The perspective directions of further investigations on improving energy efficiency of electric drives with scalar control systems are highlighted.

Abstract Objective To study the mathematical simulation analysis of shot-putter throwing optimal path. Methods Shot put was simplified as a parabolic motion of a particle, the corresponding mathematical model was established, and the mathematical relationship between the throwing distance and the initial velocity of shot put, the shooting Angle and the shooting height was defined. Results The fitting formula between shooting speed and shooting Angle was obtained by using the fitting method, and the quantitative relationship between them and the ideal shooting Angle was identified. Conclusion The mathematical principle of shot put is revealed through the process of building a model from simple to complex. However, there are still many problems to be solved, among which the height problem is a complex one. At the present level, it is not possible to find a reasonable height, because it involves many factors. However, the development of grey mathematics will provide a beneficial attempt for it to establish a reasonable and scientific model.

Introduction. The strength of construction materials when used under cyclic loads is of great importance in design engineering. A significant number of factors that affect the fatigue resistance have predetermined the creation of numerous methods that consider such influence. Nondestructive methods that are based on the connection of the physical degradation of material with strain properties enable evaluating experimentally the fatigue properties of materials. Purpose of study: the analysis of the processes of energy dissipation and strain accumulation during the inelastic cyclic strain of samples, using the VT6 (Ti-6Al-4V) titanium alloy and the D16 (Al-Cu-Mg) aluminum alloy before and after the technological impact. The work experimentally investigates the physical processes of degradation of the VT6 and D16 alloy samples that accompany the process of fatigue failure in materials with homogeneous and inhomogeneous stress-strain states in the concentrator (in the form of a hole and a weld). Typical modes are used to reach the fatigue testing that determine the critical stress in a material sample – the stress at which physical properties (temperature, strain) change without reaching the fatigue failure of samples. Critical stress amplitudes in the cycle, based on the data obtained during the experiment and the results of mathematical simulation, are compared. The effect of stress concentrators on critical loads that a detail can withstand after a unit operation is estimated by the finite-element method (FEM). As a result, the effect of the operational and technological factors on critical stress determined by strain and temperature is estimated. Comparative tests of the VT6 and D16 alloy samples with and without stress concentrators showed that the amplitudes of critical stress decrease by more than 30% in comparison with the ones that are without stress concentrators. The low-cycle fatigue tests of the D16 alloy samples are carried out. Mathematical simulation of the cyclic strain of the samples is carried out using MSC.Marc package. The results of the cyclic loading tests, which show that the characteristics of the technological process reduce the amplitudes of the critical stress of the VT6 and D16 alloys and affect the fatigue properties of the D16 aluminum alloy, are discussed. Mathematical simulation corresponded positively to the experimental data. Such correspondence indicates the possibility of conducting qualitative numerical assessments of the beginning of the inelastic strain accumulation process in structures with stress concentrators under the cyclic stress and the increasing stress amplitude, using the typical sample made of hardening elastoplastic material.

Abstract Oscillations of crystal lattices determine important material properties such as thermal conductivity, heat capacity, thermal expansion, and many others; therefore, their study is an urgent and important problem. Along with experimental studies of the nonlinear dynamics of a crystal lattice, effective computer simulation techniques such as ab initio simulation and the molecular dynamics method are widely used. Mathematical simulation is less commonly used since the calculation error there can reach 10 %. Herewith, it is the least computationally intensive. This paper describes the process and results of mathematical simulation of the nonlinear dynamics of a 3D crystal lattice of metals using the Lennard-Jones potential in the MatLab software package, which is well-proven for solving technical computing problems. The following main results have been obtained: 3D distribution of atoms over the computational cell has been plotted, proving the possibility of displacement to up to five interatomic distances; the frequency response has been evaluated using the Welch method with a relative RMS error not exceeding 30 %; a graphical dependence between the model and the reference cohesive energy data for a metal HCP cell has been obtained with an error of slightly more than 3 %; an optimal model for piecewise-linear approximation has been calculated, and its 3D interpolation built. All studies performed show good applicability of mathematical simulation to the problems of studying dynamic processes in crystal physics.

Abstract A mathematical simulation of the synthesis of butadiene rubber in a batch reactor under the action of an organolithium catalytic system in the presence of a modifier and with the addition of toluene to a solvent is carried out. A kinetic scheme of the process is proposed and the velocity constants of the elementary stages are determined on the basis of the developed model.