scholarly journals Моделирование системы определения движения технологической платформы по данным позиционирования ГЛОНАСС и измерениям ньютонометров

2019 ◽  
Vol 45 (18) ◽  
pp. 17
Author(s):  
А.С. Девятисильный ◽  
А.В. Шурыгин
Keyword(s):  
Mathematical Model ◽  
Essential Element ◽  
Numerical Differentiation ◽  
Mathematical Representations ◽  
Gravitational Forces ◽  
Discretization Step ◽  
Position Data ◽  
Motion Parameters ◽  
Limited Accuracy ◽  
Hypersonic Motion

This article presents the models for the reconstruction of linear and angular motion parameters for on-board embedded GLONASS systems with two-position data reception and a three-component newtonometer unit as measures of specific non-gravitational forces. An essential element of the construction of a mathematical model is the developed stable procedure of multiple numerical differentiation, independent of the magnitude of the discretization step of the problem under conditions of limited accuracy of calculations and measurements. The results of a numerical experiment verifying the initial physical and mathematical representations for the case of hypersonic motion are presented.

Model of Hybrid Satellite-Inertial Navigation System with Partial Structure

2019 ◽  
Vol 20 (12) ◽  
pp. 751-755
Author(s):  
A. S. Devyatisilny ◽  
A. V. Shurygin
Keyword(s):  
Mathematical Model ◽  
Navigation System ◽  
Moving Objects ◽  
Inertial Navigation ◽  
Numerical Differentiation ◽  
Basic Element ◽  
Partial Structure ◽  
Satellite Positioning ◽  
Discretization Step ◽  
And Control

A mathematical model of a hybrid navigation system (GNS) consisting of a three-component block of linear newtonometers (accelerometers) physically simulating a vector-based measurer of non-gravitational nature forces and on-board GLONASS receivers that positioning a moving object in an ellipsoidal coordinate system is presented and investigated. The absence of a gyroscopic angular velocity sensors unit, traditional for the classical schemes of the inertial navigation method, and the presence of no more than two onboard satellite positioning devices (receivers) make it possible to characterize the considered GNS as a partial structure system. As a basic element of a mathematical model for estimating linear and angular parameters of an object’s motion, the developed procedure of multiple numerical differentiation of temporal data acquired from on-board satellite receivers, which functions stably irrespective of the magnitude of the discretization step of the problem in time, was used. The developed GNS makes it possible to qualitatively evaluate both the trajectory parameters (location, velocity, acceleration and forces causing the trajectory) as well as the parameters of the spatial orientation of the object (Euler-Krylov angles and its derivatives) with a two-positioning technique. The results of the computational experiment are given. The field of application of the research results is numerical-analytical planning of trajectories, determination of motion parameters and control of moving objects for various purposes and basing.

Network analysis models – the secret for success

2004 ◽  
Vol 4 (5-6) ◽  
pp. 383-388
Author(s):  
D.M. Rogers
Keyword(s):  
Mathematical Model ◽  
Field Data ◽  
Essential Element ◽  
Distribution Networks ◽  
Automatic Calibration ◽  
Supply And Distribution ◽  
The World ◽  
Optimum Approach ◽  
Analysis Models

Water is a fundamental necessity of life. Yet water supply and distribution networks the world over are old and lacking in adequate maintenance. Consequently they often leak as much water as they deliver and provide an unacceptable quality of service to the customer. In certain parts of the world, water is available only for a few hours of the day. The solution is to build a mathematical model to simulate the operation of the real network in all of its key elements and apply it to optimise its operation. To be of value, the results of the model must be compared with field data. This process is known as calibration and is an essential element in the construction of an accurate model. This paper outlines the optimum approach to building and calibrating a mathematical model and how it can be applied to automatic calibration systems.

Parameters and States Estimates of COVID-19 Model Using Lagrange Polynomial, Least Square Approximation and Kenya Quarantine Data

2020 ◽  
pp. 25-42
Author(s):  
Cyrus Gitonga Ngari ◽  
Grace Gakii Muthuri ◽  
Mirgichan Khobocha James
Keyword(s):  
Mathematical Model ◽  
Infection Rate ◽  
Numerical Differentiation ◽  
Population Based ◽  
Least Square ◽  
Model Fit ◽  
Lagrange Polynomial ◽  
Cross Sectional ◽  
Number Of Individuals ◽  
General Community

Aims/ Objectives: To develop a compartment based mathematical model, fit daily quarantine data from Ministry of Health of Kenya, estimate individuals in latency and infected in general community and predict dynamics of quarantine for the next 90 days.Study Design: Cross-sectional study.Place and Duration of Study: 13thMarch 2020 to 30th June 2020.  Methodology: The population based model was developed using status and characteristic of COVID-19 infection. Quarantine data up to 30/6/2020 was fitted using integrating and differentiating theory of odes and numerical differentiation polynomials. Parameter and state estimates was approximated using least square. Simulations were carried out using ode Matlab solver. Daily community estimates of individuals in latency and infected were obtained together with daily estimate of rate of enlisting individual to quarantine center and their proportions were summarized.Results: The results indicated that maximum infection rate was equal 0.892999 recorded on 28/6/2020, average infection rate was 0.019958 and minimum 0.00012 on 26/6/2020.Conclusion: Predictions based on parameters and state averages indicated that the number of individuals in quarantine are expected to rise exponentially up to about 26,855 individuals by 130th day and remain constant up to 190th day.

scholarly journals Dynamic Processes of Loader Cranes Manipulators with Excessive Backlashes and Elastic Damping in Their Hinges

2019 ◽  
Vol 64 (1) ◽  
pp. 7-14
Author(s):  
Alexander V. Lagerev ◽  
Igor A. Lagerev
Keyword(s):  
Mathematical Model ◽  
Dynamic Loading ◽  
Structural Design ◽  
Impact Load ◽  
Dynamic Processes ◽  
Effective Solution ◽  
Complete Elimination ◽  
Quantitative Characteristics ◽  
Motion Parameters ◽  
Oscillatory Processes

This research is aimed at developing a mathematical model and the methodology for computer simulation of hydraulically driven manipulators of mobile cranes having excessive backlashes in cylindrical joints. The authors proposed a structural design and considered the mechanism of reducing the additional impact load in the hinges by means of elastic damping of oscillatory processes. This method allows estimating the degree of influence of the backlash and stiffness of the elastic damper on the change in the quantitative characteristics of the dynamic loading of the manipulators metalwork and the motion parameters of the transported load. While in operation, the excessive backlashes may cause an increase in the level of dynamic loading of manipulators up to 2 times or more. However, the rational choice of the elastic dampers stiffness allows an effective solution to this problem to the point of complete elimination of the additional impact load.

A Designing and Generating Method for Grinding Relief Surfaces of a Dual-Cone Double-Enveloping Hourglass Worm Gear Hob

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Chengjie Rui ◽  
Haitao Li ◽  
Jie Yang ◽  
Wenjun Wei ◽  
Xuezhu Dong
Keyword(s):  
Mathematical Model ◽  
Worm Gear ◽  
Double Cone ◽  
Grinding Wheel ◽  
Dual Cone ◽  
Generating Method ◽  
Motion Parameters ◽  
Grinding Machine ◽  
The Mathematical Model

Land widths and relief angles of a dual-cone double-enveloping hourglass worm gear hob are important factors that influence the life and the hobbing performance of the hob. Both of them are obtained by generating relief surfaces of the hob. Due to the reason that all teeth of this type of hob have different profiles with each other, all of the relief surfaces are difficult to generate for keeping all cutting teeth with uniformed relief angles and uniformed land widths. For the purpose that land widths and relief angles could be machined precisely, this paper puts forward a designing and generating method for grinding the relief surfaces. The relief surfaces are ground using the same double-cone grinding wheel as grinding the helical surfaces of the worm. Based on the theory of gearing, the mathematical model for grinding relief surfaces is built. Motion parameters when grinding the different points of the land edges on different teeth of the hob are solved. A generating simulation is built by putting those motion parameters into a four-axis hourglass worm-grinding machine. The results of the simulation show that the relief surfaces can be ground continuously and the land widths and the relief angles meet the requirements.

Control-Oriented Model of Biomimetic Underwater Vehicle Motion

2015 ◽  
Vol 236 ◽  
pp. 121-127
Author(s):  
Piotr Szymak ◽  
Tomasz Praczyk
Keyword(s):  
Mathematical Model ◽  
Research And Development ◽  
Underwater Vehicle ◽  
General Information ◽  
Development Project ◽  
National Centre ◽  
Vehicle Motion ◽  
Motion Parameters ◽  
Technology Demonstrator

In the paper, the problem of modeling motion of Biomimetic Underwater Vehicle BUV has been taken into consideration. The model of the BUV motion has been designed for initial tuning and verification of the vehicle’s autonomy system. The BUV is built within development project funded by Polish National Centre of Research and Development. At the end of the project, it is expected to achieve technology demonstrator at the 7th level of technology readiness.In the first part of the paper, a control-oriented mathematical model of the BUV designed for implementation of the simulator is described. Then, selected results of the BUV operation in the form of courses of the vehicle motion parameters are presented. Finally, general information about the implementation of the BUV model has been inserted.

A Mathematical Model for Drill Point Design and Grinding

1979 ◽  
Vol 101 (3) ◽  
pp. 333-340 ◽  
Author(s):  
W. D. Tsai ◽  
S. M. Wu
Keyword(s):  
Mathematical Model ◽  
Mathematical Representations ◽  
Drill Point ◽  
And Control

The performance of a drill is affected by the geometry of its point. The available mathematical representations of drill point geometry are inadequate to describe the variation of the drill point design. This paper develops a comprehensive mathematical model that describes the drill point geometry including the conical, the hyperboloidal, and the ellipsoidal drills. The model developed also enables one to precisely predict and control the drill point geometry and the process of grinding.

scholarly journals Study of the braking regime of rolling stock mining suspended monorail taking into account clearances in the coupling

2020 ◽  
pp. 108-115
Author(s):  
Gutarevich Viktor ◽  
◽  
Ignatkina Evgenia ◽  
Keyword(s):  
Mathematical Model ◽  
Coal Mines ◽  
Rolling Stock ◽  
Longitudinal Vibrations ◽  
Motion Parameters

Introduction. Currently, mine suspended monorails are becoming more common in coal mines for auxiliary cargo and people transportation. Compared to ground transport, monorail has significant differences, which does not allow to fully use the previously obtained results of braking modes studies. Research aims to establish regularities in the processes that occur during the mine suspended monorail road rolling stock braking mode, taking into account clearances in the couplings. Methodology. To substantiate the parameters and designs of brake and coupling devices of a mine suspended monorail, a mathematical model of rolling stock movement along the monorail has been developed. Results. Dependencies are established that describe the process of rolling stock braking on a monorail. Motion parameters for different values of stiffness, damping and clearances in the couplers are analyzed. It is established that the gaps in rolling stock coupling influence the value of undercarriage and suspension units longitudinal vibrations amplitudes. Conclusions. A mathematical model of rolling stock movement is developed with allowance for clearances in the coupling making it possible to simulate mine suspended monorail braking mode.

A PARAMETRIC MODEL OF THE PELVIC MOTION OF MIDDLE-AGED AND ELDERLY LOCOMOTION ON THE GROUND

2016 ◽  
Vol 16 (08) ◽  
pp. 1640022 ◽  
Author(s):  
LIXUN ZHANG ◽  
DA SONG ◽  
XU ZHANG ◽  
LAILU LI
Keyword(s):  
Mathematical Model ◽  
Elderly People ◽  
Walking Speed ◽  
Parametric Model ◽  
Practical Significance ◽  
Middle Aged ◽  
Movement Characteristics ◽  
Pelvic Motion ◽  
Motion Parameters

In order to study the movement characteristics of three rotational freedoms of pelvic motion during walking on the ground for middle-aged and elderly people, a mathematical model of pelvis motion was established according to the data measured. Pelvic motion parameters were studied by the Assessment of Biomechanics Functional (FAB) for 21 participants when walking at slow, normal, and fast speeds. In the experiment, multiple trajectories of the pelvis in three directions were measured, and the data were statistically analyzed with respect to the different conditions of height and walking speed. A mathematical model was established to fit the curve associated with walking speed and height. This mathematical model has practical significance for rehabilitation equipment and evaluation.

Sign in / Sign up

Export Citation Format

Share Document