scholarly journals ДЕКАРТОВА СИСТЕМА КООРДИНАТ ЯК ІНСТРУМЕНТ ПОЗИЦІОНУВАННЯ ОБ’ЄДНАНИХ ТЕРИТОРІАЛЬНИХ ГРОМАД УКРАЇНИ

2021 ◽  
pp. 30-37
Author(s):  
Інна Володимирівна Заблодська ◽  
Ксенія Ігорівна Сєрєбряк ◽  
Любов Іванівна Бєлоусова
Keyword(s):  
Sustainable Development ◽  
Coordinate System ◽  
Graphical Analysis ◽  
Practical Significance ◽  
Reference Station ◽  
Cartesian Coordinate System ◽  
Balanced Development ◽  
Social Environmental ◽  
Cartesian Coordinate ◽  
Main Material

Problem statement. The need for positioning of amalgamated territorial communities (ATC) is due to their large number and lack of identification. Effective  ATC positioning requires the development of appropriate tools to take advantage of the territory. The purpose of the article is to highlight the results of using the Cartesian system of coordination of the rear positioning of ATC in the context of their sustainable development, examples of ATC Luhansk region. The research object is ATC of Luhansk region. The methods used in the reaserch are: system, comparative and graphical analysis (the Cartesian coordinate system in space). The reaserch  hypothesis  was the preparation that the Cartesian coordinate system can be used as a tool for assessing the positions of ATCs in the context of their sustainable development. Presentation of the main material: on the basis of sustainable development estimates of  ATC of Luhansk region their positions in the Cartesian coordinate system are determined with the help of geogebra software; to determine the best positions in the  ATC of Luhansk region, it is proposed to use the vector of balanced positioning; it is established that the Lozno-Oleksandrivska  ATC has the best balanced positioning.The originality and practical significance of the reaserch polarize the propositions of vicoristic Cartesian coordinate systems for the simplest tools for controlling the positions of ATC . Conclusions and prospects fot the further reaserches. For the assessment of ATC positions, it was used a middle ball of the development by three warehouse (economy, social, environmental). The result of the positioning of ATC of the Luhansk region was filled with a rosary behind an additional Cartesian coordinate system and software geogebra protection. The positions of  ATC of the Luhansk region are displayed in the areas XOZ, XYZ, XOY. For setting the best positions at the ATC of the Luhansk region, the reference station is assigned to the vector of the balanced position, which dials up, for the most unbalanced positions from the Lozno-Oleksandrivska position. Subsequent reaserches  may be directed to the value of visits for the purpose of the balanced development of ATC.

On the Flexural-Torsional Behavior of a Straight Elastic Beam Subject to Terminal Moments

1993 ◽  
Vol 60 (2) ◽  
pp. 498-505 ◽  
Author(s):  
Z. Tan ◽  
J. A. Witz
Keyword(s):  
Coordinate System ◽  
Cross Section ◽  
Equilibrium Equation ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Elastic Beam ◽  
Cartesian Coordinate System ◽  
Kinematic Constraints ◽  
Torsional Behavior ◽  
Cartesian Coordinate

This paper discusses the large-displacement flexural-torsional behavior of a straight elastic beam with uniform circular cross-section subject to arbitrary terminal bending and twisting moments. The beam is assumed to be free from any kinematic constraints at both ends. The equilibrium equation is solved analytically with the full expression for curvature to obtain the deformed configuration in a three-dimensional Cartesian coordinate system. The results show the influence of the terminal moments on the beam’s deflected configuration.

scholarly journals A Lattice Boltzmann Scheme for Diffusion Equation in Spherical Coordinate

2018 ◽  
Vol 1 (4) ◽  
Author(s):  
Debabrata Datta ◽  
T K Pal
Keyword(s):  
Diffusion Equation ◽  
Coordinate System ◽  
Lattice Boltzmann ◽  
Spherical Coordinate System ◽  
Cartesian Coordinate System ◽  
Spherical Coordinate ◽  
Cartesian Coordinate ◽  
Lattice Boltzmann Models ◽  
Boltzmann Method ◽  
Good Agreement

Lattice Boltzmann models for diffusion equation are generally in Cartesian coordinate system. Very few researchers have attempted to solve diffusion equation in spherical coordinate system. In the lattice Boltzmann based diffusion model in spherical coordinate system extra term, which is due to variation of surface area along radial direction, is modeled as source term. In this study diffusion equation in spherical coordinate system is first converted to diffusion equation which is similar to that in Cartesian coordinate system by using proper variable. The diffusion equation is then solved using standard lattice Boltzmann method. The results obtained for the new variable are again converted to the actual variable. The numerical scheme is verified by comparing the results of the simulation study with analytical solution. A good agreement between the two results is established.

Geometrical Optics

2019 ◽  
pp. 188-214
Author(s):  
B. D. Guenther
Keyword(s):  
Coordinate System ◽  
Ray Tracing ◽  
Geometrical Optics ◽  
Paraxial Approximation ◽  
Cartesian Coordinate System ◽  
Lens System ◽  
Thin Lens ◽  
Aperture Stop ◽  
Sign Convention ◽  
Cartesian Coordinate

Discuss the limits imposed by the paraxial approximation. Define the sign convention based on the cartesian coordinate system, the foiundation of analytic geometery. Demonstrate ray tracing technique to derive the ABCD maxtrix which will generate both the gaussian and Newtonian form of the thin lens equation and the lens maker’s equation. The cardinal points of a lens are also derived. The ABCD matrix is used to explore the methods used in ray tracing to locate the aperture stop of a Cooke’s triplet lens system. In the problem set, the student is asked to use the aperture stop to locate the entrance and exit pupil of a Cooke’s triplet.

scholarly journals Approximate Inertial Coordinate System Selections for Rotation Problems - The Gravitational Field of the Celestial Body Higher than the Object Being Rotated

2015 ◽  
Vol 8 (1) ◽  
pp. 102
Author(s):  
Zifeng Li
Keyword(s):  
Gravitational Field ◽  
Coordinate System ◽  
Celestial Body ◽  
Angular Speed ◽  
Calculation Error ◽  
Cartesian Coordinate System ◽  
Inertial Coordinate System ◽  
The Earth ◽  
The Galaxy ◽  
Cartesian Coordinate

<p class="1Body">Selection of the coordinate system is essential for rotation problems. Otherwise, mistakes may occur due to inaccurate measurement of angular speed. Approximate inertial coordinate system selections for rotation problems should be the gravitational field of the celestial body higher than the object being rotated: (1) the Earth fixed Cartesian coordinate system for normal rotation problem; (2) heliocentric - geocentric Cartesian coordinate system for satellites orbiting the Earth; (3) the Galaxy Heart - heliocentric Cartesian coordinates for Earth's rotation around the Sun. In astrophysics, mass calculation error and angular velocity measurement error lead to a black hole conjecture.</p>

Three-dimensional quantum mechanics in a curved space based on the q-addition

2019 ◽  
Vol 34 (29) ◽  
pp. 1950177
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Coordinate System ◽  
Three Dimensional ◽  
One Dimension ◽  
Cartesian Coordinate System ◽  
Spherical Coordinate ◽  
Curved Space ◽  
Dimension Formula ◽  
Cartesian Coordinate

In this paper, we extend the theory of the [Formula: see text]-deformed quantum mechanics in one dimension[Formula: see text] into three-dimensional case. We relate the [Formula: see text]-deformed quantum theory to the quantum theory in a curved space. We discuss the diagonal metric based on [Formula: see text]-addition in the Cartesian coordinate system and core radius of neutron star. We also discuss the diagonal metric based on [Formula: see text]-addition in the spherical coordinate system and [Formula: see text]-deformed Heisenberg atom model.

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