MATH MODEL OF A DIRECT CURRENT MOTOR FOR STEERING ACTUATOR OF A LIQUID-PROPELLANT ENGINE

The paper presents the results of development of a math model for a direct current motor of a liquid-propellant engine steering actuator In accordance with the electrical machine theory, the math model of the motor uses a single electromagnetic coefficient. It is shown that the motor math model accuracy can be improved through the use, instead of a single electromagnetic coefficient, of two different coefficients of the math model: Electromechanical velocity coupling coefficient and torque curve coefficient. Elaborated and proposed are methods for identifying parameters of a math model of a dc motor that has natural and artificial static characteristics, which include determining its experimental static characteristics, calculating the values of static characteristics parameters using the linear regression method and calculating the values of the electric motor math model parameters using the proposed formulas. Key words: direct current electric motor, math model, parameter identification method.

Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations

In this paper we derive and analyse a class of linearly implicit schemes which includes the one of Feistauer and Kučera (J Comput Phys 224:208–221, 2007) as well as the class of RS-IMEX schemes (Schütz and Noelle in J Sci Comp 64:522–540, 2015; Kaiser et al. in J Sci Comput 70:1390–1407, 2017; Bispen et al. in Commun Comput Phys 16:307–347, 2014; Zakerzadeh in ESAIM Math Model Numer Anal 53:893–924, 2019). The implicit part is based on a Jacobian matrix which is evaluated at a reference state. This state can be either the solution at the old time level as in Feistauer and Kučera (2007), or a numerical approximation of the incompressible limit equations as in Zeifang et al. (Commun Comput Phys 27:292–320, 2020), or possibly another state. Subsequently, it is shown that this class of methods is asymptotically preserving under the assumption of a discrete Hilbert expansion. For a one-dimensional setting with some limitations on the reference state, the existence of a discrete Hilbert expansion is shown.

Dynamics of Short Recoil-Operated Weapon

In this article, the authors mentioned the function of short-recoil-operated weapons with a vertical sliding-wedge breechblock. The dynamic simulation was conducted and then the results were compared with the corresponding experimental data to verify reliability of the model. The model is calculated and tested out on the 37 mm twin anti-aircraft gun. Besides, the article presents the effect of some structural parameters on functionality of the automatic weapon. The reported results are an important theoretical basis to determine the rate of fire and the forces acting on the guns. The movement of the breechblock also affects stability of the weapon and can therefore be used to a math model or to simulate the movement of the weapon. Calculated and verified data could be used for the design of an automatic firing system as well as for solving vibration on automatic guns when burst firing.

Construction and implementation of a thermal model of aeromethane mixture combustion in the mine atmosphere, considering its kinetics

At the coal deposits exploitation by using underground methods, as a rule, negative factors that reduce coal production and miners' safety exhibit. These factors include, first of all, methane emitted from the broken coal and the coal dust as an inevitable result of work of headers and cleansing combines. Interacting with the atmosphere of mines, methane and coal dust generate dust- and dust-gas-aerial mixtures where thermophysical and chemical processes take place. First of all, these processes are combustion and detonation that until recently were included into the category of highly hazardous accidents. Based on the assumptions of single-stage chemical reaction of combustion and ideal gas agents and reaction products, an attempt to construct a math model of combustion of aeromethane mixture, considering the kinetics of chemical reaction of the origin agents. Three justified simplifying suggestions are made. The first implies that the pressure derivative is negligibly small in relation to the temperature derivative. The second implies that the area of laminar combustion consists of two zones: the mixture is being heated in one of them, and the combustion chemical reaction takes place in the other. The third implies that the temperature of mixture’s ignition does not significantly differ from the end temperature of the mixture at the completion of combustion reaction. A boundary value problem for the ordinary non-linear differential equation of the second order is set. Considering the simplifying assumptions, this was reduced to the linear equation whose solution is found in quadrature. The formulas describing combustion process have been developed. The dependences of the rate of laminar combustion on a number of mixture’s properties are established.

Dynamic Analysis of the Traffic of Vehicles Used in Car Sharing

During digitalization of transport service segment people use modern facilities such as geolocation, M2M connectivity, online payments, customer identification. We can also see a high competition here. The task of car sharing managers is to search for the optimal methods of doing business. As the regulations of business, ecological standards and technology environment of the main players is almost similar because of using the same mobile and cloud resources, it is possible to get a competitive advantage by the development of mobile apps for the employee’s PCs and smartphones of customers. The math model shown in this article is developed for implementing in digital platforms of such kind of business. This gives the opportunity to offer customers more attractive car sharing services and to reduce costs by following the environmental restrictions at the same time.

STRUCTURAL ANALYSIS OF ON-BOARD MULTIMODE AUTO TRACKING SYSTEM

Two variants of two-channel structures of tracking systems has been introduced into consideration, which are sequentially used in two modes of operation of the on-board automatic tracking system. Taking into account the fact of quantization according to the level of signals for measuring the angles of mismatch of each of the channels, it is justified to use not one, but two different structures in the second auto-tracking mode. Using mathematical modeling, the expediency of increasing the number of two-channel structures from two to three, used in a single auto-tracking process according to the criterion of the provided dynamic accuracy, have been demonstrated. This paper presents a two-channel structures investigation for tracking systems operating in tracking mode of maneuverable targets, taking into account various systems of carrier operations. Considered multichannel complex control system (CCS) structure that include precise channel (PC) and coarse channel (CC). CC use the carrier and the flight control system (FCS) to make rude tracking. The PC function implemented by an optoelectronic device (OED) has placed in a traditional angular mechanical suspension, which act with high accuracy. Described three CCS operation modes classified by target mark fall inside or outside direction finder (DF) CC or PC field of view. At the capture mode can be used only information from the CC DF. At the complex control mode becomes possible to use information from both CC DF and PC DF. At the precision mode, it is advisable to use information only from the PC DF. Developed CCS functioning math model to check main points of this work. Math model makes possible to carry out simulation tests for each mode in a separate operation, as well as when they are integrated into a single complex automatic target tracking mode. Has been described efficiency factor as the total time of satisfactory accuracy relative to entire experiment time. On math model modes efficiency has compared to each other. As result precision mode have higher efficiency and capture mode lowest. As conclusion recommended use a precision mode to achieve higher accuracy at auto tracking tasks.

CORRECTION TO THE PAPER: AN ENERGY DISSIPATIVE SPATIAL DISCRETIZATION FOR THE REGULARIZED COMPRESSIBLE NAVIER-STOKES-CAHN-HILLIARD SYSTEM OF EQUATIONS (IN MATH. MODEL. ANAL., 25(1): 110–129, HTTPS://DOI.ORG/10.3846/MMA.2020.10577)

We correct the proof of Theorem 2 in the mentioned paper concerning finite-difference equilibrium solutions.

Applications Optimal Math Model to Solve Difficult Problems for Businesses Producing and Processing Agricultural Products in Vietnam

During the months of the COVID-19 epidemic, the number of processing and manufacturing agricultural products enterprises in Vietnam faced many difficulties in the consumption of agricultural products, even when they were unable to sell. Therefore, the enterprises are more and more difficult. Many enterprises are not strong enough to restore production, so it is necessary to find solutions to overcome this difficult period. In this research, the author used the application of modern statistical techniques, along with the Grey method, to predict enterprises’ business results in the future, combined with the model of Super-slacks-based-measure efficiency (Super-SBM) to help businesses select the right partners in a supply chain to achieve their business goals. By our proposed approach, the selected solution (AG6 combined with AG10) should be implemented in the future to upgrade efficiency to help stabilize output and raise productivity; thus, both parties are able not only to improve their product quality but also achieve business goals and sustainable development. In fact, it is necessary to further this study, in combination with these factors and other quantitative models, to give investors a more comprehensive view, helping them to make the right decisions and appropriately develop their businesses and social and economic development.