Mathematical model of sea dynamics in a σ-coordinate system

2005 ◽  
Vol 20 (1) ◽  
pp. 97-113 ◽  
Author(s):  
V.B. Zalesny
Keyword(s):  
Mathematical Model ◽  
Coordinate System

scholarly journals Laboratory Stand for Simplified Verification of Missile Dynamics for Didactic Purposes

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Adam Rowicki ◽  
Grzegorz Kopecki
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Coordinate System ◽  
Second Law ◽  
Matlab Simulink ◽  
Pi Regulator ◽  
System Parameters ◽  
Proportional Integral ◽  
Roll System ◽  
Newton's Second Law

Abstract The purpose of this study was to describe dynamics of missile based on bibliography, simplify the model to the easiest form, and verify it with the use of a designed laboratory stand. Next, a simple control system of the missile was designed. The stand is prepared for didactic purposes. A mathematical model was derived by applying Newton's second law together with the earth's coordinate system and the base coordinate system. Parameters of the actual rocket model were determined using the created laboratory stand. Synthesis of the rocket roll system was designed using Simulink PID Tuner application (MathWorks, Inc. Natick, Massachusetts, USA). A control system was based on a proportional-integral (PI) regulator. The designed control system was subjected to simulated tests in MATLAB Simulink (MathWorks, Inc. Natick, Massachusetts, USA).

scholarly journals Determination of intersecting curve between two surfaces of revolution with parallel axes by use of auxiliary planes and auxiliary spheres

2002 ◽  
Vol 2 (4) ◽  
pp. 267-272
Author(s):  
Ratko Obradovic
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Coordinate System ◽  
Surfaces Of Revolution ◽  
Surface Of Revolution ◽  
First Case ◽  
Intersecting Curve

In this paper the space intersecting curve between two surfaces of revolution with parallel axes of surfaces have been determined. Two mathematical models for determination of intersecting curve between two surfaces of revolution have been formed: auxiliary planes have been used in the first mathematical model and auxiliary spheres have been used in the second model (Obradovic 2000). In the first case each auxiliary plane intersected with each surface of revolution on circle and two points of intersecting curve are obtained as intersecting points between these two circles. In the second case centres of two locks of auxiliary spheres are put on axes of surfaces of revolution (centre of first lock is on axis of the first surface of revolution and centre of second lock is on axis of the second surface of revolution) on saine z coordinate (when axes of surfaces of revolution are parallel with z axis of coordinate system). First lock sphere intersects the first surface of revolution on w1 parallels and second lock corresponding sphere intersects the second surface of revolution on w2 circles. It is possible to find a relationship that for selected radius of the first lock sphere can determine the radius of second lock sphere and real points of intersecting curve have been determined by use of these two spheres. The points of intersecting curve between two surfaces of revolution are obtained by intersection between w1 circles from the first surface with w2 circles from the second surface (Obradovic 2000).

Modeling and Calibration of Grid Structured Light Based 3-D Vision Inspection

1999 ◽  
Vol 122 (4) ◽  
pp. 734-738 ◽  
Author(s):  
Guangjun Zhang ◽  
Liqun Ma
Keyword(s):  
Mathematical Model ◽  
Coordinate System ◽  
Structured Light ◽  
Calibration Method ◽  
Experimental Results ◽  
Image Feature ◽  
Feature Analysis ◽  
Calibration Process ◽  
Vision Inspection ◽  
The Mathematical Model

The principle of structured light 3-D vision is introduced, and using projective and perspective transformations, the mathematical model of grid structured light based 3-D vision inspection is established in homogeneous coordinate system in this paper. Based on the image feature analysis of grid structured light, a calibration method of grid structured light based 3-D vision inspection is proposed, and experimental results are also presented. This method is easy, efficient and fast to carry out. It simplifies the calibration process while guaranteeing its accuracy. [S1087-1357(00)00703-6]

Study on numerical analysis of dynamic parameters of mobile walking robot

2020 ◽  
Vol 14 (1) ◽  
pp. 6380-6392 ◽  
Author(s):  
Mikhail Polishchuk ◽  
Mykyta Suyazov ◽  
Mark Opashnyansky
Keyword(s):  
Mathematical Model ◽  
Numerical Analysis ◽  
Coordinate System ◽  
Human Walking ◽  
Dynamic Parameters ◽  
Pneumatic Drive ◽  
Walking Robot ◽  
Walking Machine ◽  
Angular Coordinate ◽  
Made In

A dynamic model of a walking robot is proposed for moving along surfaces of different topologies and orientations to the horizon. The principal difference between walking robot mechanisms is that they are made in the form of flexible pedipulators. Actually the pedipulators are a set of spherical rings with a hydraulic or pneumatic drive. The patented design (Patent UA No 117065, publ. 2018.06.11) of the robot's feet is anthropomorphic and allows the robot to work in the angular coordinate system inherent in the human walking machine. The proposed mathematical model allows us to calculate the dynamic parameters (forces and moments) and compare these parameters with the allowable technological load that a walking robot can perform without losing adhesion with the displacement surface.

scholarly journals Mathematical model of landslide stable equilibrium

Vestnik MGSU ◽  
2019 ◽  
pp. 1292-1298
Author(s):  
Vladimir V. Simonyan ◽  
Alexey A. Kochiev
Keyword(s):  
Mathematical Model ◽  
Coordinate System ◽  
Sliding Surface ◽  
Force Vector ◽  
Rectangular Coordinate System ◽  
The Real ◽  
Objective Information ◽  
Landslide Stability ◽  
Landslide Body ◽  
Landslide Movement

Introduction. A definition of landslide stability condition is given for any sliding surfaces, density, mass, volume, slope, i.e., in general. As a result of mathematical analysis, equilibrium equations in coordinates are obtained. When violating any of these conditions, the landslide movement begins. The problem is in the way of obtaining real parameter values entering the equations. The mechanical and mathematical model of a landslide having an arbitrary sliding surface is the subject of the study. The aim is determining a time of landslide movement beginning and central issues in the task of landslide prediction. Materials and methods. A standard rectangular coordinate system with the origin at the vertex of the landslide body surface was chosen. A derivation of the equation of the landslide body equilibrium in coordinates was given through the equation of surface in general, through the normal friction force vector in components of the coordinate axes and the traction force vector in components of the coordinate axes. Results. The conditions of landslide stability were obtained. The most critical problems were identified. The solution to these problems can lead to the development of theoretical and practical methods for predicting landslide processes, which is very important for solving the problems of ensuring the safety of buildings and structures located on the slope areas. Conclusions. It is necessary to set the real values of all the parameters, to identify the shape of the sliding surface, to determine the real parameters of the landslide body, and correctly position the rectangular coordinate system. The most close approach to solving these problems is possible in case of applying the methods of integrated approach to the analysis of landslide slope area stability, which includes an engineering and geological method (a method of obtaining objective information about the physical and mechanical characteristics of soils on landslide areas of the investigated slope) and an engineering and geodetic method (a method of obtaining objective information about the terrain, area and slope). Acknowledgements: The authors express their gratitude to the reviewers.

scholarly journals STUDY OF TRANSIENT AND STATIONARY OPERATION MODES OF SYNCHRONOUS SYSTEM CONSISTING IN TWO MACHINES

2017 ◽  
Vol 60 (3) ◽  
pp. 228-236
Author(s):  
V. S. Safaryan
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Power System ◽  
Mathematical Models ◽  
Coordinate System ◽  
Electric Power ◽  
Electric Power System ◽  
Machine System ◽  
Transient Regimes ◽  
The Mathematical Model

The solution of the problem of reliable functioning of an electric power system (EPS) in steady-state and transient regimes, prevention of EPS transition into asynchronous regime, maintenance and restoration of stability of post-emergency processes is based on formation and realization of mathematical models of an EPS processes. During the functioning of electric power system in asynchronous regime, besides the main frequencies, the currents and voltages include harmonic components, the frequencies of which are multiple of the difference of main frequencies. At the two-frequency asynchronous regime the electric power system is being made equivalent in a form of a two-machine system, functioning for a generalized load. In the article mathematical models of transient process of a two-machine system in natural form and in d–q coordinate system are presented. The mathematical model of two-machine system is considered in case of two windings of excitement at the rotors. Also, in the article varieties of mathematical models of EPS transient regimes (trivial, simple, complete) are presented. Transient process of a synchronous two-machine system is described by the complete model. The quality of transient processes of a synchronous machine depends on the number of rotor excitation windings. When there are two excitation windings on the rotor (dual system of excitation), the mathematical model of electromagnetic transient processes of a synchronous machine is represented in a complex form, i.e. in coordinate system d, q, the current of rotor being represented by a generalized vector. In asynchronous operation of a synchronous two-machine system with two excitation windings on the rotor the current and voltage systems include only harmonics of two frequencies. The mathematical model of synchronous steady-state process of a two-machine system is also provided, and the steady-state regimes with different structures of initial information are considered.

scholarly journals SIMPLIFIED MATHEMATICAL MODEL OF A MAGNETIC SYSTEM WITH A CIRCULAR MAGNETIC CONDUCTOR

2021 ◽  
Author(s):  
Yuriy Kreselyuk ◽  
Anastasiya Ivzhenko ◽  
Mihail Kirsa
Keyword(s):  
Mathematical Model ◽  
Magnetic Flux ◽  
Coordinate System ◽  
Magnetic System ◽  
Magnetic Core ◽  
Cylindrical Coordinate System ◽  
Magnetic Conductor ◽  
Rectangular Coordinate System ◽  
Cylindrical Coordinate ◽  
Simplified Mathematical Model

A simplified design of a magnetic system with a circular magnetic core is presented and its mathematical model is developed to determine the magnetic flux. Transition from a cylindrical coordinate system to a rectangular coordinate system.

scholarly journals Mathematical Model of Human Semicircular Canal Spatial Attitude 

2021 ◽  
Author(s):  
Shu-zhi Wu ◽  
Ping Lin ◽  
Yan-yan Zheng ◽  
Yi-fei Zhou ◽  
Xiao-kai Yang
Keyword(s):  
Mathematical Model ◽  
Coordinate System ◽  
Semicircular Canal ◽  
Average Method ◽  
Vestibular Function ◽  
Semicircular Canals ◽  
Normal Vector ◽  
Spatial Coordinate ◽  
Average Value ◽  
Plane Normal

Abstract Located deep in the temporal bone, the semicircular canal is a subtle structure that requires a spatial coordinate system for measurement and observation. In this study,Fifty-five semicircular canal and eyeball models were obtained by segmentation of MRI data. The spatial coordinate system was established by taking the top of the common crus and the bottom of eyeball as the horizontal plane. Firstly, the plane equation is calculated according to the centerline of the semicircular canals. Then, according to the parameters of the plane equation, the plane normal vectors are obtained. Finally, the average unit normal vector of each semicircular canal plane can be obtained by calculating the average value of the vectors. It is more intuitive and accurate to calculate the average normal vector of semicircular canal plane with the vector average method, which is different from the angular average method in different degrees. The mathematical model of semicircular canal spatial attitude established in this study is more reliable, which can guide the vestibular function examination, and also help guide the diagnosis and treatment of BPPV.

A Mathematical "Screw-Nut" Connection Model for the Universal Software to Analyse Dynamical Systems

2017 ◽  
pp. 1-12
Author(s):  
V. A. Martynyuk ◽  
V. A. Trudonoshin ◽  
V. G. Fedoruk
Keyword(s):  
Mathematical Model ◽  
Coordinate System ◽  
Dry Friction ◽  
Local Coordinate System ◽  
Direction Cosine ◽  
The Body ◽  
Global Coordinate System ◽  
Elastic Model ◽  
Screw Axis ◽  
The Mathematical Model

The article deals with a mathematical model of the "screw-nut" connection adapted for using in universal software systems to analyse dynamic characteristics. This article is sequel to a number of earlier authors-written articles devoted to object simulation of 3D mechanics. Such a model available in the library of mathematical models of the modelling system will significantly extend the list of simulated mechanisms. The mathematical model of "screw-nut" connection suggests such a connection between absolutely rigid bodies. The "screw-nut" connection parameters are the following:thread pitch by the radian of the angle of pitch;coordinates of the point on the axis of the screw in the local coordinate system of the body 1;direction cosines of the screw axis in the local coordinate system of the body 1.Note that the connection parameters have constant values. Two drawbacks of this model should be noted.1. Some expressions of the mathematical model involve dividing by direction cosine  of the screw axis thereby eliminating "division by zero" when the axis of the screw is perpendicular to the x-axis of the global coordinate system. The software-based way allows eliminating this shortcoming.2. The model does not include coordinates of mass centres of bodies tied by connection. This can lead to a significant "mismatch" in the position of the bodies in modelling of multi- periodic transient processes. However, adding an elastic model to the mathematical model can eliminate this drawback.The article demonstrates the "screw-nut" connection model to simulate a jack using the PA8 system and comparing its results with those obtained with help of the NX10 complex. Gives, in addition, the results of influence in terms of dry friction in the "screw-nut" connection. Taking into consideration the dry friction allows us to reflect the effect of "self-stopping" in the jack.

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