scholarly journals Two-Dimensional Cartesian Coordinate System Educational Toolkit: 2D-CACSET

Sensors ◽  
2021 ◽  
Vol 21 (18) ◽  
pp. 6304
Author(s):  
Víctor H. Castañeda-Miranda ◽  
Luis F. Luque-Vega ◽  
Emmanuel Lopez-Neri ◽  
Jesús Antonio Nava-Pintor ◽  
Héctor A. Guerrero-Osuna ◽  
...  
Keyword(s):  
Coordinate System ◽  
Wide Band ◽  
Modern Technology ◽  
Two Dimensional ◽  
Cartesian Coordinate System ◽  
Education Benefits ◽  
And Mathematics ◽  
Cartesian Coordinate ◽  
Constructing Knowledge ◽  
And Control

Engineering education benefits from the application of modern technology, allowing students to learn essential Science, Technology, Engineering, and Mathematics (STEM) related concepts through hands-on experiences. Robotic kits have been used as an innovative tool in some educational fields, being readily accepted and adopted. However, most of the time, such kits’ knowledge level requires understanding basic concepts that are not always appropriate for the student. A critical concept in engineering is the Cartesian Coordinate System (CCS), an essential tool for every engineering, from graphing functions to data analysis in robotics and control applications and beyond. This paper presents the design and implementation of a novel Two-Dimensional Cartesian Coordinate System Educational Toolkit (2D-CACSET) to teach the two-dimensional representations as the first step to construct spatial thinking. This innovative educational toolkit is based on real-time location systems using Ultra-Wide Band technology. It comprises a workbench, four Anchors pinpointing X+, X−, Y+, Y− axes, seven Tags representing points in the plane, one listener connected to a PC collecting the position of the Tags, and a Graphical User Interface displaying these positions. The Educational Mechatronics Conceptual Framework (EMCF) enables constructing knowledge in concrete, graphic, and abstract levels. Hence, the students acquire this knowledge to apply it further down their career path. For this paper, three instructional designs were designed using the 2D-CACSET and the EMCF to learn about coordinate axes, quadrants, and a point in the CCS.

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>

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