scholarly journals A Mathematical Model for Top Motions

2019 ◽  
Vol 2 (4) ◽  
Keyword(s):  
Mathematical Model ◽  
Angular Momentum ◽  
Mathematical Models ◽  
Analytical Approach ◽  
Fundamental Principle ◽  
Educational Process ◽  
Coriolis Forces ◽  
Inertial Torque ◽  
Long Time ◽  
Gyroscopic Effects

The topic of the top motions is not new but the known publications represent wrong mathematical models for its gyroscopic effects. Recent investigations have demonstrated the physics of gyroscopic effects is more complex. On any spinning objects are acting the system of interrelated internal torques generated by their rotating mass elements and center mass. The inertial torque is produced by the centrifugal, common inertial and Coriolis forces, as well as the change in the angular momentum. These inertial torqueses represent the fundamental principle of gyroscope theory. The new inertial torques enables deriving mathematical models for the motions of any rotating objects that were impossible for a long time. The aim of this work is to represent mathematical models for the motions of the well-balanced top on the flat horizontal surface. This work describes the physics of the top motions and closes the problem of many years of discussion. The new analytical approach for the top’s motions definitely responds to the practical results and represents a good example of the educational process.

scholarly journals A Mathematical Model for Top Nutation Based on Inertial Forces of Distributed Masses

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Ryspek Usubamatov ◽  
Albina Omorova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Angular Momentum ◽  
Mathematical Models ◽  
Vibration Analysis ◽  
Analytical Approach ◽  
Main Property ◽  
Inertial Forces ◽  
Applied Torque ◽  
Dynamics And Vibration

The main property of gyroscopic devices is maintaining the axis of a spinning rotor, a mathematical model formulated on the principle of the change in the angular momentum. This principle is used for mathematical modeling of the motions of a top at known publications. Nevertheless, practical tests of gyroscopic devices do not correspond to this analytical approach. Recent investigations have demonstrated that the origin of gyroscope properties is more complex than that represented in known publications. The applied torque on a gyroscope produces internal torques of the spinning rotor based on the action of the several inertial forces. These forces are the centrifugal, Coriolis, and common inertial forces as well as the change in the angular momentum generated by the mass elements and center-mass of the spinning rotor. The action of these torques manifests itself in the resistance and precession torques of the gyroscopic devices. These inertial torques act simultaneously and interdependently around two axes and represent the fundamental principles of the gyroscope theory. The new inertial torques enable deriving mathematical models for the motions of well-known top that is the simplest form of gyroscopic devices. The novelty of the work is mathematical models for the motions of the top based on action of eight inertial forces acting around its two axes. The obtained mathematical models for the top nutation and self-stabilization are represented in terms of machine dynamics and vibration analysis. The new analytical approach for motions of the well-balanced top and top with eccentricity of the center-mass definitely responds to the practical results.

scholarly journals Inertial Forces Acting on a Propeller of Aircraft

2018 ◽  
Vol 7 (1) ◽  
pp. 1-13
Author(s):  
R. Usubamatov ◽  
T. Zhumaev
Keyword(s):  
Angular Momentum ◽  
Mathematical Models ◽  
Inertial Forces ◽  
Aerospace Vehicles ◽  
Coriolis Forces ◽  
Rotating Blades ◽  
Variable Resistance ◽  
Combined Action ◽  
The Masses ◽  
Physical Principles

Background:Aerospace vehicles use propellers with the different design that possess gyroscopic properties. Recent investigations in the area of gyroscope theory have demonstrated that the gyroscope properties are based on the action of the centrifugal, common inertial, and Coriolis forces of the distributed mass elements of the spinning rotor, as well as the change in the angular momentum.Objective:The combined action of the interrelated inertial forces on the propellers presents the interests for the design of the blades. The objective of the manuscript is the derivation of mathematical models for the inertial torques acting on the spinning propellers that enable computing the stresses of the blades and increasing their reliability.Method:The inertial torques generated by the masses of the rotating blades acting on the propellers are represented by mathematical models in L. Euler’s form.Results:The inertial torques are generated by the several inertial forces of the propeller’s blades and hub and manifested the fluctuation of the variable resistance and precession torques acting around different axes of the propeller. Derived mathematical models for the inertial torques are new and should be used for the computing forces and stresses acting on the propellers of the aircraft.Conclusion:The mathematical models for the torques acting on the propellers consider the several inertial forces of the rotating masses that manifest their gyroscope properties. Derived mathematical models for inertial torques enable for computing the stresses of the aircraft propellers and clearly demonstrate the physical principles and origin of the acting inertial forces.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

A mathematical model and an algorithm for sampling sets of components on the Assembly enterprises of space technology

2018 ◽  
Vol 15 (1) ◽  
pp. 39-55
Author(s):  
V. B. Rudakov ◽  
V. M. Makarov ◽  
M. I. Makarov
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Space Technology ◽  
Economic Costs ◽  
Problem Statement ◽  
Optimal Plan ◽  
Product Mix ◽  
Technical Parameters ◽  
Complex Products ◽  
Assembly Plants

The article considers the problem of determining the rational plans of the input sampling reliability and technical parameters of components of space technology, the totality of which is supplied to the Assembly plants for the manufacture of complex products of space technology. Problem statement and mathematical model based on the minimization of the economic costs of control and losses related to the risks of taking wrong decisions, are given in the article. The properties of the mathematical models are investigated, the algorithm for its optimization is developed. The result is an optimal plan for the sampling of sets of components, which includes: an optimal product mix subject to mandatory control of the aggregate and optimum risks of first and second kind, when acceptance number of statistical plan is zero. The latter circumstance is due to the high requirements of reliability and technical parameters of products of space technology.

scholarly journals An Efficient Analytical Approach to Visualize Text-Based Event Logs for Semiconductor Equipment

2021 ◽  
Vol 11 (13) ◽  
pp. 5944
Author(s):  
Gunwoo Lee ◽  
Jongpil Jeong
Keyword(s):  
Complex System ◽  
Analytical Approach ◽  
System Behavior ◽  
File Size ◽  
Log Files ◽  
Event Logs ◽  
Hard Disk Space ◽  
Long Time ◽  
Log File ◽  
Runtime Information

Semiconductor equipment consists of a complex system in which numerous components are organically connected and controlled by many controllers. EventLog records all the information available during system processes. Because the EventLog records system runtime information so developers and engineers can understand system behavior and identify possible problems, it is essential for engineers to troubleshoot and maintain it. However, because the EventLog is text-based, complex to view, and stores a large quantity of information, the file size is very large. For long processes, the log file comprises several files, and engineers must look through many files, which makes it difficult to find the cause of the problem and therefore, a long time is required for the analysis. In addition, if the file size of the EventLog becomes large, the EventLog cannot be saved for a prolonged period because it uses a large amount of hard disk space on the CTC computer. In this paper, we propose a method to reduce the size of existing text-based log files. Our proposed method saves and visualizes text-based EventLogs in DB, making it easier to approach problems than the existing text-based analysis. We will confirm the possibility and propose a method that makes it easier for engineers to analyze log files.

Research on cargo-loading optimization based on genetic and fuzzy integration

2021 ◽  
Vol 40 (4) ◽  
pp. 8493-8500
Author(s):  
Yanwei Du ◽  
Feng Chen ◽  
Xiaoyi Fan ◽  
Lei Zhang ◽  
Henggang Liang
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Three Dimensional ◽  
Distribution Center ◽  
Long Time ◽  
Low Efficiency ◽  
Decision Making Model ◽  
The Mathematical Model ◽  
Loading Scheme

With the increase of the number of loaded goods, the number of optional loading schemes will increase exponentially. It is a long time and low efficiency to determine the loading scheme with experience. Genetic algorithm is a search heuristic algorithm used to solve optimization in the field of computer science artificial intelligence. Genetic algorithm can effectively select the optimal loading scheme but unable to utilize weight and volume capacity of cargo and truck. In this paper, we propose hybrid Genetic and fuzzy logic based cargo-loading decision making model that focus on achieving maximum profit with maximum utilization of weight and volume capacity of cargo and truck. In this paper, first of all, the components of the problem of goods stowage in the distribution center are analyzed systematically, which lays the foundation for the reasonable classification of the problem of goods stowage and the establishment of the mathematical model of the problem of goods stowage. Secondly, the paper abstracts and defines the problem of goods loading in distribution center, establishes the mathematical model for the optimization of single car three-dimensional goods loading, and designs the genetic algorithm for solving the model. Finally, Matlab is used to solve the optimization model of cargo loading, and the good performance of the algorithm is verified by an example. From the performance evaluation analysis, proposed the hybrid system achieve better outcomes than the standard SA model, GA method, and TS strategy.

Rapid determination of glomerular filtration rate by single-bolus inulin: a comparison of estimation analyses

1998 ◽  
Vol 84 (6) ◽  
pp. 2154-2162 ◽  
Author(s):  
Cord Sturgeon ◽  
Albert D. Sam ◽  
William R. Law
Keyword(s):  
Mathematical Model ◽  
Glomerular Filtration Rate ◽  
Mathematical Models ◽  
Glomerular Filtration ◽  
Filtration Rate ◽  
Rapid Determination ◽  
Constant Infusion ◽  
Sprague Dawley ◽  
Single Bolus ◽  
Sprague Dawley Rats

Rapid measurement of glomerular filtration rate (GFR) by an inulin single-bolus technique would be useful, but its accuracy has been questioned. We hypothesized that reported inaccuracies reflect the use of inappropriate mathematical models. GFR was measured in 14 intact and 5 unilaterally nephrectomized conscious male Sprague-Dawley rats (mean weight 368 ± 12 g) by both single-bolus (25 mg/kg) and constant-infusion techniques (0.693 mg ⋅ kg−1 ⋅ min−1). The temporal decline in plasma inulin concentration was analyzed through biexponential curve fitting, which accounted for renal inulin loss before complete vascular and interstitial mixing. We compared our mathematical model based on empirical rationale with those of other investigators whose studies suggest inaccuracy of single-bolus methods. Our mathematical model yielded GFR values by single bolus that agreed with those obtained by constant infusion [slope = 0.94 ± 0.16 (SE); y intercept = 0.23 ± 0.64; r = 0.82]. In comparison to the data obtained by constant inulin infusion, this method yielded a very small bias of −0.0041 ± 0.19 ml/min. Two previously reported models yielded unsatisfactory values (slope = 1.46 ± 0.34, y intercept = 0.47 ± 1.5, r = 0.72; and slope = 0.17 ± 1.26, y intercept = 17.15 ± 5.14, r = 0.03). The biases obtained by using these methods were −2.21 ± 0.42 and −13.90 ± 1.44 ml/min, respectively. The data indicate that when appropriate mathematical models are used, inulin clearance after single-bolus delivery can be used to measure GFR equivalent to that obtained by constant infusion of inulin. Attempts to use methods of analysis for simplicity or expediency can result in unacceptable measurements relative to the clinical range of values seen.

Twin Models

1970 ◽  
Vol 19 (1-2) ◽  
pp. 141-141
Author(s):  
L. Gedda ◽  
G. Brenci ◽  
M. T. Lun
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Genetic Parameters ◽  
Simultaneous Recording ◽  
Theoretical Relationship ◽  
Twin Models

The theoretical relationship between the distribution of a given trait in a population of twin pairs and several genetic parameters has been examined. In particular, a series of mathematical models has been worked out, that, when applied to a twin population, nonselected for the occurrence of a given trait and nondiagnosed as to zygosity, leads to an estimate of:1) The MZ: DZ ratio in the population;2) The frequency of the genotype responsible for a given trait;3) The probability of manifestation of the trait;4) The value of epistatic factors.A further mathematical model affords the estimate of linkage in the hypothesis of simultaneous recording of more than one trait.

Neurotechnology as a factor of the educational process transformation

2021 ◽  
pp. 98-13
Author(s):  
Л.Д. Александрова ◽  
Р.А. Богачева ◽  
Т.А. Чекалина ◽  
М.В. Максимова ◽  
В.И. Тимонина
Keyword(s):  
Effective Means ◽  
Individual Characteristics ◽  
Educational Process ◽  
Special Equipment ◽  
Research Areas ◽  
Long Time ◽  
Mental Abilities ◽  
The Individual ◽  
And Control

Изучение возможностей мозга для повышения качества обучения находится в центре внимания педагогической науки уже много лет. Развитие цифровизации позволило использовать в исследованиях специальное оборудование, с помощью которого можно оценивать и контролировать работу мозга, развивать умственные способности, познавательные функции и т. п. Нейротехнологии стали эффективным средством, позволяющим трансформировать образовательный процесс за счет подбора специального учебного контента с учетом индивидуальных особенностей обучающихся. Вместе с тем возникает необходимость в конкретизации терминологии и определении актуальных направлений исследований в данной области. For a long time, the study of the brain capabilities for the improvement of the quality of education has been an urgent direction in pedagogical science. Due to the development of digitalization, new areas of research have emerged related to the use of special equipment that makes it possible to assess and control brainwork, develop mental abilities, cognitive functions, etc. One of them is neurotechnology, which is an effective means of transforming the educational process: it offers educational content based on the individual characteristics of students. Thus, a need to concretize the terminology and determine the current research areas arises. The article aims to attempt to fill this gap with the help of a representative analysis of publications on neurotechnologies, as well as the essence of neuroeducation.

Numerical modelling of swirling momentumless turbulent wake dynamics

2018 ◽  
pp. 37-48
Author(s):  
Андрей Геннадьевич Деменков ◽  
Геннадий Георгиевич Черных
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Equations Of Motion ◽  
Turbulent Wake ◽  
The Body ◽  
Jet Flows ◽  
Reynolds Stresses ◽  
Bodies Of Revolution ◽  
Averaged Equations

С применением математической модели, включающей осредненные уравнения движения и дифференциальные уравнения переноса нормальных рейнольдсовых напряжений и скорости диссипации, выполнено численное моделирование эволюции безымпульсного закрученного турбулентного следа с ненулевым моментом количества движения за телом вращения. Получено, что начиная с расстояний порядка 1000 диаметров от тела течение становится автомодельным. На основе анализа результатов численных экспериментов построены упрощенные математические модели дальнего следа. Swirling turbulent jet flows are of interest in connection with the design and development of various energy and chemical-technological devices as well as both study of flow around bodies and solving problems of environmental hydrodynamics, etc. An interesting example of such a flow is a swirling turbulent wake behind bodies of revolution. Analysis of the known works on the numerical simulation of swirling turbulent wakes behind bodies of revolution indicates lack of knowledge on the dynamics of the momentumless swirling turbulent wake. A special case of the motion of a body with a propulsor whose thrust compensates the swirl is studied, but there is a nonzero integral swirl in the flow. In previous works with the participation of the authors, a numerical simulation of the initial stage of the evolution of a swirling momentumless turbulent wake based on a hierarchy of second-order mathematical models was performed. It is shown that a satisfactory agreement of the results of calculations with the available experimental data is possible only with the use of a mathematical model that includes the averaged equations of motion and differential equations for the transfer of normal Reynolds stresses along the rate of dissipation. In the present work, based on the above mentioned mathematical model, a numerical simulation of the evolution of a far momentumless swirling turbulent wake with a nonzero angular momentum behind the body of revolution is performed. It is shown that starting from distances of the order of 1000 diameters from the body the flow becomes self-similar. Based on the analysis of the results of numerical experiments, simplified mathematical models of the far wake are constructed. The authors dedicate this work to the blessed memory of Vladimir Alekseevich Kostomakha.

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