scholarly journals Vector Products As A Tool For The Investigation Of The Isometric Transformation Of Objects

2015 ◽  
Vol 98 (1) ◽  
pp. 60-71
Author(s):  
Ryszard Józef Grabowski
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Necessary Condition ◽  
Vector Product ◽  
Isometric Transformation ◽  
Check Points ◽  
Normal Vectors ◽  
Definition Of ◽  
Three Dimensional Space

Abstract The identification of isometric displacements of studied objects with utilization of the vector product is the aim of the analysis conducted in this paper. Isometric transformations involve translation and rotation. The behaviour of distances between check points on the object in the first and second measurements is a necessary condition for the determination of such displacements. For every three check points about the measured coordinate, one can determine the vector orthogonal to the two neighbouring sides of the triangle that are treated as vectors, using the definition of the vector product in three-dimensional space. If vectors for these points in the first and second measurements are parallel to the studied object has not changed its position or experienced translation. If the termini of vectors formed from vector products treated as the vectors are orthogonal to certain axis, then the object has experienced rotation. The determination of planes symmetric to these vectors allows the axis of rotation of the object and the angle of rotation to be found. The changes of the value of the angle between the normal vectors obtained from the first and second measurements, by exclusion of the isometric transformation, are connected to the size of the changes of the coordinates of check points, that is, deformation of the object. This paper focuses mainly on the description of the procedure for determining the translation and rotation. The main attention was paid to the rotation, due to the new and unusual way in which it is determined. Mean errors of the determined parameters are often treated briefly, and this subject requires separate consideration.

Dynamic Simulation of Multibody Mechanical Systems Using the Vector-Network Model

1988 ◽  
Vol 12 (1) ◽  
pp. 21-30 ◽  
Author(s):  
M.J. Richard
Keyword(s):  
Dynamic Models ◽  
Analytical Procedure ◽  
Dimensional Space ◽  
Digital Simulation ◽  
Three Dimensional ◽  
General Purpose ◽  
New Approach ◽  
Network Method ◽  
Definition Of ◽  
Three Dimensional Space

Pressing technological problems have created a growing interest in the development of dynamic models for the digital simulation of multibody systems. This paper describes a new approach to the problem of motion prediction. An extension of the “vector-network” method to rigid body systems in three-dimensional space is introduced. The entire procedure is a basic application of concepts of graph theory in which laws of vector dynamics are combined. The analytical procedure was successfully implemented within a general-purpose digital simulation program since, from a minimal definition of the mechanism, it will automatically predict the behavior of the system as output, thereby giving the impression that the equations governing the motion of the mechanical system have been completely formulated and solved by the computer. Simulations of the response of a rail vehicle which demonstrate the validity, applicability and self-formulating aspect of the automated model are provided.

Determination of the modulated structure of Sr14/11CoO3 through a (3 + 1)-dimensional space description and using non-harmonic ADPs

1999 ◽  
Vol 55 (6) ◽  
pp. 841-848 ◽  
Author(s):  
O. Gourdon ◽  
V. Petricek ◽  
M. Dusek ◽  
P. Bezdicka ◽  
S.  Durovic ◽  
...  
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Atomic Displacement ◽  
Atomic Displacement Parameter ◽  
Third Order ◽  
Modulated Structure ◽  
New Phase ◽  
Space Description ◽  
Three Dimensional Space

Sr14/11CoO3 (i.e. Sr14Co11O33, tetradecastrontium undecacobalt tritriacontaoxide), a new phase in the hexagonal perovskite Sr x CoO3 system, has been prepared and its structure solved from single-crystal X-ray data within the (3 + 1)-dimensional formalism. Sr14/11CoO3 crystallizes in the trigonal symmetry, R3¯m(00γ)0s superspace group with the following lattice parameters: as = 9.508 (2), cs = 2.5343 (7) Å, q = 0.63646 (11)c * and Vs = 198.40 (13) Å3. With the commensurate versus incommensurate test not being conclusive, the structure was considered as commensurate (P32 three-dimensional space group), but refined within the (3 + 1)-dimensional formalism to a residual factor R = 0.0351 for 47 parameters and 1169 independent reflections. Crenel functions were used for the oxygen and cobalt description and a Gram–Charlier expansion up to the third order of the atomic displacement parameter was employed for one Co atom. The structure is similar to that of Sr6/5CoO3, but with a different sequence of the octahedra and trigonal prism polyhedra along the [CoO3] chains. An interesting feature evidenced by the non-harmonic expansion is the displacement of the prismatic Co atoms from the site center, towards the prism rectangular faces.

scholarly journals Ideals of Herzog–Northcott type

2011 ◽  
Vol 54 (1) ◽  
pp. 161-186 ◽  
Author(s):  
Liam O'Carroll ◽  
Francesc Planas-Vilanova
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Regular Sequence ◽  
Point Of View ◽  
Prime Ideals ◽  
Monomial Curves ◽  
Definition Of ◽  
Minimal Prime ◽  
Special Case ◽  
Three Dimensional Space

AbstractThis paper takes a new look at ideals generated by 2×2 minors of 2×3 matrices whose entries are powers of three elements not necessarily forming a regular sequence. A special case of this is the ideals determining monomial curves in three-dimensional space, which were studied by Herzog. In the broader context studied here, these ideals are identified as Northcott ideals in the sense of Vasconcelos, and so their liaison properties are displayed. It is shown that they are set-theoretically complete intersections, revisiting the work of Bresinsky and of Valla. Even when the three elements are taken to be variables in a polynomial ring in three variables over a field, this point of view gives a larger class of ideals than just the defining ideals of monomial curves. We then characterize when the ideals in this larger class are prime, we show that they are usually radical and, using the theory of multiplicities, we give upper bounds on the number of their minimal prime ideals, one of these primes being a uniquely determined prime ideal of definition of a monomial curve. Finally, we provide examples of characteristic-dependent minimal prime and primary structures for these ideals.

Determination of Sound Velocity in Three-Dimensional Space by Optical Probe

2008 ◽  
Vol 47 (5) ◽  
pp. 3959-3961 ◽  
Author(s):  
Takeshi Ohbuchi ◽  
Koichi Mizutani ◽  
Naoto Wakatsuki ◽  
Hiroyuki Masuyama
Keyword(s):  
Sound Velocity ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Optical Probe ◽  
Three Dimensional Space

In Vivo Determination of the Direction of Rotation and Moment-Angle Relationship of Individual Elbow Muscles

1998 ◽  
Vol 120 (5) ◽  
pp. 625-633 ◽  
Author(s):  
L. Zhang ◽  
J. Butler ◽  
T. Nishida ◽  
G. Nuber ◽  
H. Huang ◽  
...  
Keyword(s):  
Muscle Activation ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Elbow Flexion ◽  
Joint Movement ◽  
Flexion Extension ◽  
Relationship Of ◽  
Three Dimensional Space

The direction of rotation (DOR) of individual elbow muscles, defined as the direction in which a muscle rotates the forearm relative to the upper arm in three-dimensional space, was studied in vivo as a function of elbow flexion and forearm rotation. Electrical stimulation was used to activate an individual muscle selectively, and the resultant flexion-extension, supination-pronation, and varus-valgus moments were used to determine the DOR. Furthermore, multi-axis moment-angle relationships of individual muscles were determined by stimulating the muscle at a constant submaximal level across different joint positions, which was assumed to result in a constant level of muscle activation. The muscles generate significant moments about axes other than flexion-extension, which is potentially important for actively controlling joint movement and maintaining stability about all axes. Both the muscle DOR and the multi axis moments vary with the joint position systematically. Variations of the DOR and moment-angle relationship across muscle twitches of different amplitudes in a subject were small, while there were considerable variations between subjects.

scholarly journals Un modelo para visualizar objetos en 4D con el Mathematica

2018 ◽  
pp. 51-58
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Higher Dimensions ◽  
Two Dimensional ◽  
3D Objects ◽  
El Sistema ◽  
Definition Of ◽  
Three Dimensional Space

Un modelo para visualizar objetos en 4D con el Mathematica A model to visualize objects in 4D with Mathematica Ricardo Velezmoro y Robert Ipanaqué Universidad Nacional de Piura, Urb. Miraflores s/n, Castilla, Piura, Perú.  DOI: https://doi.org/10.33017/RevECIPeru2014.0008/ Resumen Una variedad de técnicas de gráficos por computadora han permitido la visualización de objetos, que existen en dimensiones más altas, en una pantalla 2D. En este artículo se propone un nuevo modelo a partir de la extensión de una técnica útil en la visualización de objetos en 3D en una pantalla 2D para realizar algo similar con objetos en 4D. Dicha técnica se basa en la definición de una inmersión, en primera instancia, del espacio tridimensional en el espacio bidimensional que luego se toma como referencia para definir otra inmersión, que constituye el modelo propuesto en este artículo, del espacio tetra dimensional en el espacio tridimensional. En teoría la visualización de objetos en 4D en una pantalla 2D se consigue mediante la composición de las dos inmersiones mencionadas, pero en la práctica se aprovechan los comandos incorporados en el sistema de cálculo simbólico Mathematica para tal fin. Descriptores: objetos 4D, modelo, inmersión Abstract A variety of computer graphics techniques have enabled the display of objects, which exist in higher dimensions, on a 2D screen. In this paper a new model from the extension of a technique useful in visualizing 3D objects on a 2D screen to make something similar with 4D objects is proposed. This technique is based on the definition of a immersion, in the first instance, from the three-dimensional space in two-dimensional space which is then taken as a reference to define another immersion, which is the model proposed in this paper, from the fourdimensional space in three dimensional space. Theoretically the visualization of objects in 4D on a 2D screen is achieved by the composition of the two immersions mentioned, but in practice the incorporated commands into the computer algebra system Mathematica for this purpose are utilized. Keywords: objects 4D, model, immersion.

scholarly journals Design, the Decoration of Culture?

IDEA JOURNAL ◽  
1969 ◽  
pp. 71-84
Author(s):  
Tom Loveday
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Necessary Condition ◽  
Built Form ◽  
Material Substance ◽  
Interior Designers ◽  
Architecture And Design ◽  
Investigative Process ◽  
Three Dimensional Space ◽  
Material Substances

Interior designers have tended, like architects, to determine three-dimensional space using geometry by manipulating representations of material substances or building work. Geometry without substance is of thought only and only has one quantity; number. As such design becomes the manipulation of representations with the traditions of geometry. One of those traditions is the understanding of geometry as pure static Cartesian abstraction impurely expressed in substance. Design has tended to do this for a number of reasons, one of which is to engage more fully with the design of built form and another is to distance itself from decoration. This paper explores the issue and asks three questions: Is the repetition of Enlightenment geometry a necessary condition for architecture and design? If it is, does material substance become merely an excessive characteristic of pure concepts conceived as pure abstract geometry? Is culture becoming so dependent on geometry that to make geometry a pure abstraction is to understand material substance as excessive? These questions are reformulated through the investigative process of the paper and are asked in a different form as a conclusion.

Determination of Arbitrary Tooth Displacements

1978 ◽  
Vol 57 (5-6) ◽  
pp. 663-674 ◽  
Author(s):  
R.J. Pryputniewicz ◽  
C.J. Burstone ◽  
W.W. Bowley
Keyword(s):  
Dimensional Space ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Double Exposure ◽  
Maxillary Central Incisor ◽  
Modern Technique ◽  
Hologram Interferometry ◽  
Component Loading ◽  
Three Dimensional Space

The noninvasive, modern technique based on the method of double-exposure hologram interferometry was used to measure arbitrary displacements of teeth in the three dimensional space. The experimental studies were carried out on an idealized model of the maxillary central incisor. The results show that the experimental data, based on component loading, are inadequate to accurately predict tooth displacement from an arbitrary force acting in the three dimensional space.

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