scholarly journals The Problem of Two Bodies with a Finite Velocity of Gravity

2019 ◽  
pp. 160-164
Author(s):  
Vasyl Slyusarchuk
Keyword(s):  
Mathematical Model ◽  
Gravitational Field ◽  
Mathematical Apparatus ◽  
Universal Gravitation ◽  
Finite Velocity ◽  
Delay Argument ◽  
Velocity Of Light ◽  
The Moment ◽  
The Mathematical Model ◽  
Two Bodies

From the moment of Newton’s discoveryof the law of universal gravitation, ordinary differentialequations were used to study the motion of bodies,since it was assumed that the velocity of gravitationis infinite. However, in reality the velocity of gravityis finite, which is consistent with the theory of relativityof Einstein, which postulated that the velocity ofgravity matches the velocity of light, and the studiesconducted by S. Kopeikin and E. Fomalont on the fundamentallimit of the velocity of gravity. Due to thedelay of the gravitational field for studying the motionof bodies, the mathematical apparatus based on differentialequations with a delay argument is the mostacceptable one. These equations are used to constructand study the mathematical model of the motion of twobodies. It is shown that the motion of these bodies withidentical masses (with finite velocity of gravity!) is notcarried out in accordance with Kepler’s laws.

scholarly journals INVESTIGATION OF THE INFLUENCE OF PRESSING BELTS TENSION OF THE BACK CIRCUIT OF PRESS - SELECTIVE PR-1.5

2018 ◽  
Vol 13 (2) ◽  
pp. 76-76
Author(s):  
Валерий Белов ◽  
Valeriy Belov ◽  
Леонид Рыбаков ◽  
Leonid Rybakov ◽  
Светлана Овчукова ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Experimental Studies ◽  
Field Research ◽  
Test Protocol ◽  
Optimal Value ◽  
The Stability ◽  
The Moment ◽  
The Mathematical Model ◽  
Elastic Characteristics

A brief analysis of suspension mechanisms and ways to improve the quality of press harvesting for flax harvesting is considered. By researching the mathematical model, the authors prove the possibility of increasing the stability of the elastic characteristics of the suspension mechanisms by changing the angle between the levers or changing the geometry of the structure, for example, the attachment point of a two-arm lever. Particular attention is drawn to the new term “reduced rigidity” of the suspension mechanism. Using this notion and the method of its determination, the authors recommend determining the optimal value of the reduced stiffness of the suspension in the way of mathematical modeling and using this indicator as the main optimization parameter. The results of theoretical and experimental studies were presented by the authors in the form of elastic characteristics of the suspension mechanisms. When conducting a study of the mathematical model, it is suggested to take into account the condition of equality of the maximum values of the moments of forces from the action of the tension forces of the belts or the mass of the working element and the moment of forces acting on the side of the tension springs. During the research of the suspension mechanism, the actual dimensions of the PR-1.5 baler design were adopted. At the same time, we briefly describe the design of the improved tensioning mechanism of a baler for flax harvesting. A rather detailed analysis is given by the authors of the obtained elastic characteristics of the suspension mechanism. Some new features of the elastic characteristics of the suspension mechanism that have not been previously detected are described. To confirm the correctness of the reasoning, the authors implemented their research in a real press-picker and conducted field research that confirmed the possibility of improving the quality of the upgraded version of the machine. To confirm the results of the research, the authors presented a fragment of the field test protocol. The task is solved, uniformity of the roll density is ensured and its density is increased.

Probabilistic model of structural phase transition in perovskites

2021 ◽  
pp. 2150211
Author(s):  
S. H. Jabarov ◽  
R. T. Aliyev ◽  
N. A. Ismayilova
Keyword(s):  
Mathematical Model ◽  
Phase Transitions ◽  
Crystal Structures ◽  
Structural Phase ◽  
Random Variable ◽  
Structural Phase Transitions ◽  
The Moment ◽  
The Mathematical Model ◽  
First Time

In this work, the crystal structures and phase transitions of compounds with perovskite structure were investigated. The classification of structural phase transitions in perovskites was carried out, the most common crystal structures and structural phase transitions were shown. A mathematical model was constructed, a theorem was given and proved for the probability of a possible transition. The formulas [Formula: see text] and [Formula: see text] are given for the mathematical expectation and variance of random variable [Formula: see text], which is the moment when the stochastic process [Formula: see text] deviation from the boundary [0, [Formula: see text]] interval for the first time. According to the mathematical model, one of the trajectories of random processes corresponding to the phase transitions that occur in perovskites is constructed.

scholarly journals DEVELOPMENT OF MATHEMATICAL MODEL OF THE CONTROL SYSTEM OF LINKS OF THE SNAKE LIKE ROBOT

2016 ◽  
Vol 2 (1) ◽  
pp. 150-154
Author(s):  
Гладышев ◽  
Andrey Gladyshev ◽  
Алейников ◽  
Andrey Aleynikov ◽  
Афонин ◽  
...  
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Control System ◽  
Transfer Function ◽  
Transfer Functions ◽  
Modular Control ◽  
The Moment ◽  
External Forces ◽  
The Mathematical Model ◽  
Angle Of Rotation

The mathematical model of a modular control system of links of the snake like robot for realization of the wave movement considering the moments of the external forces created by adjacent links and external indignations is given in work. As model of the electric drive of a direct current the differential equation of the second order connecting tension of u(t) given on the electric motor, the moment of loading of Mn (t) and an output angle of rotation of a shaft θ(t) is used. Transfer functions of separate links are calculated, and transfer function of a control system in general is received.

scholarly journals Mathematical model for estimation the stability of the vehicle's motion on overturning

2021 ◽  
pp. 47-52
Author(s):  
Serhii Povaliaiev ◽  
Olexii Saraiev
Keyword(s):  
Mathematical Model ◽  
Traffic Accidents ◽  
Order Differential Equation ◽  
Road Traffic ◽  
Center Of Mass ◽  
Conservation Of Energy ◽  
The Stability ◽  
The Moment ◽  
The Mathematical Model ◽  
Vehicle Movement

Problem. During the reconstruction of the circumstances of road traffic accidents with vehicles overturning, difficulties arise with determining the parameters of vehicles in the process of their overturning. This is due to the fact that the recommended calculation methods are often simplified. The main focus of such techniques is to determine the minimum speed of vehicles, which leads to their overturning. In fact, the speed of vehicles before overturning can be significantly higher. Goal. This paper is dedicated to developing mathematical model of overturning vehicles that makes possible to determine not only the conditions for overturning vehicles, but also other parameters of the vehicle movement in the process of overturning. Methodology. The overturning of the vehicle occurs as a result of the action of inertial forces after collision with an immovable side obstacle. In this case, the moment from the force of gravity of the vehicle keeps it from overturning. In the process of overturning the vehicle, the moment from the force of gravity decreases due to the decrease in the arm of the force of gravity. To compile a mathematical model, the basic equation of dynamics during rotational motion was used. The mathematical model of a vehicle overturning is written in the form of a nonlinear homogeneous second order differential equation. An analytical solution of this equation is obtained. Results. Developed mathematical model makes possible to determine not only the conditions for overturning vehicles, but also other parameters of the vehicle movement from the moment the center of mass begins to rise to the moment of its maximum rise in the process of overturning. For a particular case, when the critical speed of a vehicle during its overturning is determined, the developed mathematical model fully corresponds to the mathematical model based on the law of conservation of energy. For a specific vehicle, numerical results were obtained that fully correspond to the physics of the overturning process.

scholarly journals Experimental calibration of the mathematical model of Air Torque Position dampers with non-cascading blades

2016 ◽  
Vol 20 (2) ◽  
pp. 567-578
Author(s):  
Sinisa Bikic ◽  
Dusan Uzelac ◽  
Masa Bukurov ◽  
Milivoj Radojcin ◽  
Ivan Pavkov
Keyword(s):  
Mathematical Model ◽  
Air Flow ◽  
Operating Conditions ◽  
Air Velocity ◽  
Experimental Calibration ◽  
Laboratory Facility ◽  
Different Types ◽  
The Moment ◽  
Air Conditioning Systems ◽  
The Mathematical Model

This paper is focused on the mathematical model of the Air Torque Position dampers. The mathematical model establishes a link between the velocity of air in front of the damper, position of the damper blade and the moment acting on the blade caused by the air flow. This research aims to experimentally verify the mathematical model for the damper type with non-cascading blades. Four different types of dampers with non-cascading blades were considered: single blade dampers, dampers with two cross-blades, dampers with two parallel blades and dampers with two blades of which one is a fixed blade in the horizontal position. The case of a damper with a straight pipeline positioned in front of and behind the damper was taken in consideration. Calibration and verification of the mathematical model was conducted experimentally. The experiment was conducted on the laboratory facility for testing dampers used for regulation of the air flow rate in heating, ventilation and air conditioning systems. The design and setup of the laboratory facility, as well as construction, adjustment and calibration of the laboratory damper are presented in this paper. The mathematical model was calibrated by using one set of data, while the verification of the mathematical model was conducted by using the second set of data. The mathematical model was successfully validated and it can be used for accurate measurement of the air velocity on dampers with non-cascading blades under different operating conditions.

scholarly journals Operational Optimization of the Electromechanical System in Non-deterministic Conditions

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Technical Problem ◽  
Control Object ◽  
Electromechanical System ◽  
Operational Optimization ◽  
The Moment ◽  
Definition Of ◽  
The Impact ◽  
The Mathematical Model

On the basis of theoretical and practical studies of the electromechanical system, the scientific and technical problem of improving the control system of the electromechanical system during the impact on it of multi-vector perturbations is solved. The result of the study is the integration of differential equations with coefficients dependent on the oscillations of the control object. In the theoretical part, the mathematical model of the electromechanical system was synthesized, which made it possible to investigate ways of minimizing the deviation angles and time intervals required to stabilize the motion of the electromechanical system, which allowed indirectly to realize the associated signal with the stochastic nature of the moment of oscillation of the control object on the coordinate plane. The method of parametric optimization of the mathematical model of the electromechanical system in the function of the angle of inclination is also improved and investigated. Based on the definition of the structure and algorithms of work, the efficiency of the control system of the electromechanical system increases in terms of reducing the stabilization time of the control object.

scholarly journals Law of universal gravitation with finite velocity of gravity and mathematical model of motion of a finite number of material points

2020 ◽  
pp. 120-123
Author(s):  
Vasyl Slyusarchuk
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Finite Number ◽  
Ordinary Differential Equations ◽  
Classical Model ◽  
Universal Gravitation ◽  
Finite Velocity ◽  
Deviating Argument ◽  
The Law ◽  
Material Points

The law of universal gravitation is intro- duced taking into account the finiteness of the gravi- tational velocity. Based on this law, a mathematical model of the motion of a finite number of material points is constructed, a separate case of which is the classical model of the motion of points, which is de- scribed by a system of ordinary differential equations. The constructed model is a system of nonlinear dif- ferential equations with deviating argument and func- tional equations. It more accurately describes the dy- namics of a finite number of material points than the corresponding classical model. A mathematical model of the motion of two material points is also considered.

Wind Generator Model for Fault Diagnosis

2013 ◽  
Vol 347-350 ◽  
pp. 1430-1434
Author(s):  
Wei Wang ◽  
Hai Fang Yu ◽  
Chang Fu Zheng ◽  
Yan Shi Zhao
Keyword(s):  
Mathematical Model ◽  
Fault Diagnosis ◽  
Wind Turbine ◽  
Synchronous Generator ◽  
Equation Model ◽  
Generator Voltage ◽  
Drive Chain ◽  
The Moment ◽  
Tower Vibration ◽  
The Mathematical Model

In order to make a diagnosis of wind turbine failure, the mathematical model of the wind turbine should be prepared. This model can provide a theoretical basis for fault diagnosis. establishing the mathematical model of the main part of the generator being discussed on theoretical ,including the tower vibration, wind wheel and drive chain, the moment of inertia of the wind turbine and the synchronous generator voltage equation model in dq coordinate system. Its main focus on the demand for wind turbine fault diagnosis.

scholarly journals Mathematical model of orientation of a ferromagnetic particle in magnetic field

2018 ◽  
Vol 224 ◽  
pp. 02041
Author(s):  
Eugene Masyutkin ◽  
Vasilii Masyagin ◽  
Boris Avdeyev
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Homogeneous Magnetic Field ◽  
System Of Differential Equations ◽  
Medium Resistance ◽  
The Moment ◽  
Fourth Order Method ◽  
Driving Torque ◽  
The Mathematical Model ◽  
Angle Of Rotation

A mathematical model of the rotational motion of a particle with pronounced ferromagnetic properties, due to the moment of forces from the side of an external homogeneous magnetic field is deduced in the article. The basis of the model is the equation for the moment of forces effecting on a solid body. The driving torque is the magnetic moment, calculated through the strength of the external field and the magnetization of the material. The counter–torque is the moment of medium resistance, which mainly depends on the viscosity of the medium in which the simulated body is located. The dependences of the angle of rotation and angular velocity on time are determined. The mathematical model is represented as a system of differential equations. The developed mathematical model was solved by a Runge – Kutta fourth order method. The obtained results are presented in the form of graphs.

scholarly journals MATHEMATICAL MODEL FOR DETERMINING THE STEP TIME AND DISTANCE COVERED BY THE DROPLETS OF LUQUID FIRE-FIGHTING AGENT DURING THE PROCESS OF FIRE EXTINGUISHING IN THE CLOSED ROOM

Fire Safety ◽  
2018 ◽  
pp. 63-68
Author(s):  
O. Ukhanska ◽  
N. Shtangret
Keyword(s):  
Mathematical Model ◽  
Effective Mass ◽  
Horizontal Plane ◽  
Experimental Studies ◽  
Fire Fighting ◽  
Effective Diameter ◽  
Fire Extinguishing ◽  
The Moment ◽  
The Mathematical Model

The article deals with the mathematical model for determining the step time and distance covered by the droplet of liquid till the moment of contact with the horizontal plane. Numerical values of the step time and distance covered till the moment of contact with the horizontal plane are obtained. Experimental studies aimed on determining the effective diameter of the droplet are performed. According to effective diameter value an effective mass of the droplet is determined. After obtaining the effective mass value the step time and distance covered by the droplet of liquid till the moment of contact with the horizontal plane are calculated using a mathematical model.

Sign in / Sign up

Export Citation Format

Share Document