scholarly journals External ballistics howitzer projectile

2021 ◽  
pp. 13-20
Author(s):  
Lev Velychko ◽  
Oksana Petruchenko ◽  
Oksana Tereshchuk ◽  
Roman Nanivskyi
Keyword(s):  
Differential Equations ◽  
Initial Velocity ◽  
Initial Conditions ◽  
Functional Dependence ◽  
System Of Differential Equations ◽  
Kinematic Parameters ◽  
Projectile Velocity ◽  
Firing Range ◽  
Air Resistance ◽  
The Impact

In this scientific work, the team of authors presents a mathematical model for studying the dynamics of the motion of a projectile in the air, fired from cannon. One of the main problems of external ballistics is to determine the magnitude of the force of the air resistance to the movement of the projectile. Usually in studies, a discrete relationship between the magnitude of the force of resistance and projectile velocity has been established. However, to improve the accuracy of firing, it is necessary to determine the functional dependence of air resistance on projectile velocity, deterministic and non-deterministic factors. The authors, when processing the results of landfill studies, which are presented in the tables of firing, found that the magnitude of the force of air resistance to the movement of the projectile depends not only on its speed but also on acceleration Based on this, the functional dependence of the force of air resistance is described separately during the movement of the projectile with the following velocities: supersonic (stage I); subsonic - with negative acceleration (stage II); subsonic with positive acceleration (stage III). To determine the coefficients of functional dependences, it is proposed to use inverse dynamics problems. Boundary conditions were considered - the full horizontal range of the projectile, depending on the specific angle of impact, obtained from the results of landfill research and given in the firing tables. Under the condition of a certain functional dependence of the force of counter-air resistance, taking into account the weight of the projectile and the Carioles’ force, as a result of this work is obtained the system of differential equations, which describes the motion of the projectile in air. The initial conditions for the first stage were taken the initial velocity of the projectile and zero (original) coordinates; for the second stage - the value of the kinematic parameters of the projectile at a time when its speed became equal to the speed of sound in the air; for the third stage - the value of the kinematic parameters of the projectile at the time when its velocity began to increase. By solving the system of differential equations, using the appropriate software, can be determined the impact of projectile charge and air temperatures, atmospheric pressure, changes in projectile mass and its initial velocity on the kinematic parameters of projectile motion. In addition, it allows you to automate the process of determining the aiming angle (it is better to ask the gunners the correctness of this concept) depending on the firing range, taking into account the above factors. Also, in the work on the basis of the method proposed by the authors, the is carried out comparison of the kinematic parameters of the projectile with the results given in the firing tables. They indicate minor differences when shooting at short distances, but when shooting at long distances - these differences increase, as the results in the tables of shootings are quite approximate.

Elaboration of stochastic models to comprehensive evaluation of occupational risks in complex dynamic systems

2021 ◽  
Vol 1 (104) ◽  
pp. 31-41
Author(s):  
A.P. Bochkovskyi
Keyword(s):  
Differential Equations ◽  
Markov Processes ◽  
Stochastic Models ◽  
Comprehensive Evaluation ◽  
System Of Differential Equations ◽  
Partial Derivatives ◽  
Occupational Risks ◽  
The Impact ◽  
Negative Factors ◽  
Over Time

Purpose: Elaborate stochastic models to comprehensive evaluation of occupational risks in “man - machine - environment” systems taking into account the random and dynamic nature of the impact on the employee of negative factors over time. Design/methodology/approach: Within study, the methods of probability theory and the theory of Markov processes - to find the limit distribution of the random process of dynamic impact on the employee of negative factors over time and obtain main rates against which the level of occupational risks within the "man - machine - environment" systems can be comprehensively evaluated; Erlang phases method, Laplace transform, difference equations theory, method of mathematical induction - to elaborate a method of analytical solution of the appropriate limit task for a system of differential equations in partial derivatives and appropriate limit conditions were used. Findings: A system of differential equations in partial derivatives and relevant limit conditions is derived, which allowed to identify the following main rates for comprehensive evaluation of occupational risks in systems "man - machine - environment": probability of excess the limit of the employee's accumulation of negative impact of the harmful production factor; probability of the employee’s injury of varying severity in a random time. An method to the solution the limit task for a system of differential equations, which allows to provide a lower bounds of the probability of a certain occupational danger occurrence was elaborated. Research limitations/implications: The elaborated approach to injury risk evaluation is designed to predict cases of non-severe injuries. At the same time, this approach allows to consider more severe cases too, but in this case the task will be more difficult. Practical implications: The use of the elaborated models allows to apply a systematic approach to the evaluation of occupational risks in enterprises and to increase the objectivity of the evaluation results by taking into account the real characteristics of the impact of negative factors on the employee over time. Originality/value: For the first time, a special subclass of Markov processes - Markov drift processes was proposed and substantiated for use to comprehensive evaluation of occupational risks in “man - machine - environment” systems.

scholarly journals ЗОВНІШНЯ БАЛІСТИКА СНАРЯДУ БМ1 ВИПУЩЕНОГО З Т-12 (МТ-12)

World Science ◽  
2020 ◽  
Vol 1 (1(53)) ◽  
pp. 23-29
Author(s):  
Величко Лев Дмитрович ◽  
Горчинський Ігор Володимирович ◽  
Сорокатий Микола Іванович
Keyword(s):  
Atmospheric Pressure ◽  
Sound Speed ◽  
Functional Dependence ◽  
Resistance Force ◽  
Kinematic Parameters ◽  
Muzzle Velocity ◽  
Velocity Magnitude ◽  
Air Resistance ◽  
The Mathematical Model

The magnitudes of the kinematic parameters of projectiles motion in the air depends on deterministic (form of projectile, its mass, temperature of air and charge, atmospheric pressure, derivation) and nondeterministic (muzzle velocity, magnitude and direction of wind velocity) values. During the projectile movement, its weight and frontal air resistance force have a determining influence on its dynamics. In the article it is investigated proposed by authors the mathematical model of determination of the functional dependence of the magnitude of the frontal air resistance force of the projectile’s motion on its velocity, mass and caliber, geometric characteristics, temperature and density of air, atmospheric pressure, sound speed in air. Since the trajectory of movement of the BM1 projectile released from the T-12 (MT-12) is canopy, it is assumed that during the projectile’s flight the air temperature and atmospheric pressure are unchanged and equal to their value at the point of the gun.

scholarly journals ESTIMATING THE INFLUENCE OF THE WIND EXPOSURE ON THE MOTION OF AN EXTINGUISHING SUBSTANCE

2020 ◽  
Vol 5 ◽  
pp. 51-59
Author(s):  
Yuriy Abramov ◽  
Oleksii Basmanov ◽  
Valentina Krivtsova ◽  
Andrii Khyzhnyak
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Wind Effect ◽  
System Of Differential Equations ◽  
Wind Action ◽  
Fire Extinguishing ◽  
Additive Component ◽  
Wind Exposure ◽  
Using Data

One of the tasks to be solved when deploying fire extinguishing systems is to determine the range of the fire extinguishing agent supply to the combustion center. This problem is solved using data on the trajectory of the fire-extinguishing agent in the combustion center. The presence of wind impact on the process of supplying a fire extinguishing agent will lead to a change in its trajectory. To take into account wind impact, it becomes necessary to assess the result of such impact. Using the basic equation of dynamics for specific forces, a system of differential equations is obtained that describes the delivery of a fire extinguishing agent to the combustion center. The system of differential equations takes into account the presence of wind impact on the movement of the extinguishing agent. The presence of wind action is taken into account by the initial conditions. To solve such a system, the integral Laplace transform was used in combination with the method of undefined coefficients. The solution is presented in parametric form, the parameter of which is time. For a particular case, an expression is obtained that describes the trajectory of the supply of the extinguishing agent into the combustion center. Nomograms are constructed, with the help of which the operative determination of the estimate of the maximum range of the fire-extinguishing agent supply is provided. Estimates are obtained for the time of delivery of a fire-extinguishing agent to the combustion center, and it is shown that for the characteristic parameters of its delivery, this value does not exceed 0.5 s. The influence of wind action on the range of supply of a fire extinguishing agent is presented in the form of an additive component, which includes the value of the wind speed and the square of the time of its delivery. To assess the effect of wind impact on the movement of the fire extinguishing agent, an analytical expression for the relative error was obtained and it was shown that the most severe conditions for supplying the fire extinguishing agent to the combustion center, the value of this error does not exceed 5.5%. Taking into account the wind effect when assessing the range of supply of a fire-extinguishing agent makes it possible to increase the efficiency of fire-extinguishing systems due to its more accurate delivery to the combustion center

Three-Dimensional Frictional Rigid-Body Impact

1995 ◽  
Vol 62 (4) ◽  
pp. 893-898 ◽  
Author(s):  
V. Bhatt ◽  
Jeff Koechling
Keyword(s):  
Differential Equations ◽  
Rigid Body ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Local Analysis ◽  
Integration Scheme ◽  
Numerical Integration Scheme ◽  
Rigid Body Model ◽  
Global Nature ◽  
The Impact

We present an analysis of the rigid-body model for frictional three-dimensional impacts, which was originally studied by Routh. Using Coulomb’s law for friction, a set of differential equations describing the progress and outcome of the impact process for general bodies can be obtained. The differential equations induce a flow in the tangent velocity space for which the trajectories cannot be solved for in a closed form, and a numerical integration scheme is required. At the point of sticking, the numerical problem becomes ill-conditioned and we have to analyze the flow at the singularity to determine the rest of the process. A local analysis at the point of sticking provides enough information about the global nature of the flow to let us enumerate all the possible dynamic scenarios for the sliding behavior during impact. The friction coefficient, and the mass parameters at the point of contact, determine the particular sliding behavior that would occur for a given problem. Once the initial conditions are specified, the possible outcome of the impact can then be easily determined.

scholarly journals Investigation of iceberg towing processes based on finite-dimensional models of continuous media

2020 ◽  
pp. 82-88
Author(s):  
В.А. Коршунов ◽  
Р.С. Мудрик ◽  
Д.А. Пономарев ◽  
А.А. Родионов
Keyword(s):  
Numerical Modeling ◽  
Differential Equations ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Mathematical Formulation ◽  
Element Model ◽  
Dynamic Factor ◽  
System Of Differential Equations ◽  
Finite Dimensional ◽  
Simplified Algorithm

В работе рассмотрена проблема управления ледовой обстановкой при освоении участков на морской шельфе. Отмечено, что наиболее эффективным способом управления движения айсбергов и их осколков является использование буксировочных систем. В зависимости от размера айсберга в качестве буксировочной системы может использоваться либо одиночный канат, либо ледовая сетка. Описана технология осуществления буксировки. Рассмотрено два варианта математической формулировки задачи буксировки. Инженерный подход основан на решении системы нелинейных дифференциальных уравнений динамики с известными начальными условиями. Наиболее точным является аппарат механики сплошных сред, который опирается на фундаментальные законы сохранения. Он позволяет построить связанную нелинейную систему дифференциальных уравнений с минимальным количеством допущений. Использование данного подхода возможно при численном моделировании процесса буксировки. В работе создана конечно-элементная модель взаимодействия айсберга с буксировочной системой. Разработан упрощенный алгоритм учета жидкости. Получены кинематические и динамические характеристики процесса буксировки. Определен коэффициент динамичности усилий. The paper deals with the problem of ice management during the development of the sea shelf. It is noted that the most effective way to control the movement of icebergs and their fragments is to use towing systems. Depending on the size of the iceberg, either a single rope or an ice net can be used as a towing system. The technology of towing is described. Various of the mathematical formulation of the towing problem are considered. The engineering approach is based on solving a system of nonlinear differential equations of dynamics with initial conditions. More accurate approach is the computational continuum mechanics, which is based on fundamental conservation laws. It allows to build a nonlinear system of differential equations with a minimum of assumptions. This approach can be used for numerical modeling of the towing process. In the paper, a finite element model of the interaction of an iceberg with a towing system is created. To account liquid the simplified algorithm is prescribed. The kinematic and dynamic characteristics of the towing process are obtained. The dynamic factor of axial force is determined.

scholarly journals Determining the loose medium movement parameters in a centrifugal continuous mixer using a discrete element method

2021 ◽  
Vol 3 (7 (111)) ◽  
pp. 59-67
Author(s):  
Volodymyr Statsenko ◽  
Oleksandr Burmistenkov ◽  
Tetiana Bila ◽  
Svitlana Demishonkova
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Discrete Element Method ◽  
Pearson Correlation ◽  
Discrete Element ◽  
System Of Differential Equations ◽  
Continuous Action ◽  
Centrifugal Mixer ◽  
The Impact ◽  
Element Method

The processes to form the compositions of loose materials in centrifugal mixers of continuous action have been considered. Based on the method of discrete elements, a mathematical model of the movement of particles in the rotor of the centrifugal mixer was built, taking into consideration their geometric and physical-mechanical parameters. To assess the extent of influence of these parameters on the nature of particle movement, a well-known mathematical model in the form of a system of differential equations was used, which was built on the basis of classical laws of mechanics. The process of mixing particles of two loose materials under different initial conditions of movement was modeled. The trajectories of individual particles along the bottom and side wall of the rotor were calculated. The results of the research reported here have established that the model built on the basis of the discrete element method makes it possible to improve the accuracy of determining the parameters of the movement of loose materials in the mixing zone. Calculations that involved this method show that the length of the particle trajectory is 2.9, and the movement time is 9 times greater than those calculated by the system of differential equations. The built and known mathematical models demonstrated the same nature of the distribution of components in the mixer. The value of the Pearson correlation coefficient between the calculated values of the coefficients of variation is 0.758. The best homogeneity is achieved by separating the flows of the mixture components and reducing the distance between their centers. The experimental study was carried out using a centrifugal mixer of continuous action with a conical rotor. Particle trajectories were constructed; it was established that the shape of the trajectory built by a discrete element method is closer to the experimental one. The results reported in this paper make it possible to predict the impact of the structural and technological parameters of the mixers of continuous action on the uniformity of the mixture

scholarly journals Selectively caring for the most severe COVID-19 patients delays ICU bed shortages more than increasing hospital capacity

2020 ◽  
Author(s):  
Miles Roberts ◽  
Helena Duplechin Seymour ◽  
Alexander Dimitrov ◽  
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Mortality Data ◽  
System Of Differential Equations ◽  
Infection Rates ◽  
Us States ◽  
Hospital Capacity ◽  
Hospital Resources ◽  
Parameter Values ◽  
Implementing Strategies

1AbstractSARS-CoV-2, the virus responsible for COVID-19, has killed hundreds of thousands of Americans. Although physical distancing measures played a key role in slowing COVID-19 spread in early 2020, infection rates are now peaking at record levels across the country. Hospitals in several states are threatened with overwhelming numbers of patients, compounding the death toll of COVID-19. Implementing strategies to minimize COVID-19 hospitalizations will be key to controlling the toll of the disease, but non-physical distancing strategies receive relatively little attention. We present a novel system of differential equations designed to predict the relative effects of hospitalizing fewer COVID-19 patients vs increasing ICU bed availability on delaying ICU bed shortages. This model, which we call SEAHIRD, was calibrated to mortality data on two US states with different peak infection times from mid-March – mid-May 2020. It found that hospitalizing fewer COVID-19 patients generally delays ICU bed shortage more than a comparable increase in ICU bed availability. This trend was consistent across both states and across wide ranges of initial conditions and parameter values. We argue that being able to predict which patients will develop severe COVID-19 symptoms, and thus require hospitalization, should be a key objective of future COVID-19 research, as it will allow limited hospital resources to be allocated to individuals that need them most and prevent hospitals from being overwhelmed by COVID-19 cases.

scholarly journals Vibration of the Biomass Boiler Tube Excited with Impact of the Cleaning Device

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1519
Author(s):  
Dragan Cveticanin ◽  
Nicolae Herisanu ◽  
Istvan Biro ◽  
Miodrag Zukovic ◽  
Livija Cveticanin
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equation ◽  
Mode Shapes ◽  
Straight Beam ◽  
Special Cases ◽  
Cleaning Device ◽  
The Impact

In boilers with biomass fuel, a significant problem is caused due to the slag layer formed from the unburned particles during combustion. In the paper, a tube cleaning method from slag is proposed. The method is based on the impact effect of the end of the tube with the aim to produce vibration for slag elimination. The tube is modeled as a clamped-free nonlinear oscillatory system. The initial impact of the tube causes vibrations. The mathematical model of the system is a nonlinear partial differential equation with zero initial deflection. To obtain the ordinary differential equations, the Galerkin method is applied. By discretizing the equation into a finite degree of freedom system, using the undamped linear mode shapes of the straight beam as basic functions, the reduced order model, consisting of ordinary differential equations in time, is obtained. The ordinary time equations are analytically solved by adopting the Krylov–Bogoliubov procedure. Special cases of nonlinear differential equations are investigated. In the paper, the influence of the nonlinear parameters and initial conditions on the vibration properties of the tube is obtained. We use the procedure developed in the paper and the analytical results for computation of the impact parameters of the cleaning device.

scholarly journals DYNAMIC MODEL OF A SOCIALLY RESPONSIBLE ENTERPRISE POTENTIAL

2018 ◽  
pp. 245-252
Author(s):  
Liudmyla Potrashkova
Keyword(s):  
Differential Equations ◽  
Dynamic Models ◽  
Production Capacity ◽  
Causal Chain ◽  
System Of Differential Equations ◽  
Socially Responsible ◽  
Proposed Model ◽  
Environmental Projects ◽  
Environmental Measures ◽  
The Impact

Introduction. Socially responsible measures, which are implemented by the enterprise, launch a complex chain of cause and effect links in the resource system of the enterprise. Therefore, to analyse the impact of such measures on the dynamics of enterprise resources, as well as to address the task of assessing the potential of a socially responsible enterprise, it is necessary to use dynamic models that will describe the specified chain of causal relationships. Purpose. The article aims to construct a model of the dynamics of characteristics of the resources of a socially responsible enterprise in the form of a system of differential equations, as well as to determine the possibility of using such a model for solving the task of assessing the potential of the enterprise. Result. In order to achieve this goal, a system of differential equations is developed. This system describes the dynamics of the characteristics of the resources of an environmentally responsible enterprise, which carries out projects to improve the ecological characteristics of its products and processes. An important feature of the proposed model is that it takes into account the causal chain of the impact of environmental measures on the dynamics of enterprise resources. On the one hand, environmental projects divert funds from projects to increase production capacity. On the other hand, due to the ecological responsibility of consumers, environmental projects positively influence the amount of specific profit per unit of production of the enterprise. Conclusions. The implementation of the proposed model for various variants of the values of controlled parameters allows us to find the set of Pareto-optimal values of the vector of the result indicators of the enterprise's activity. This set is a result of the evaluation of the potential of the analysed enterprise. The inclusion in the proposed model of the cause-effect chain of the impact of environmental measures on the dynamics of resources increases the accuracy of the assessment of the potential of a socially responsible enterprise.

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