scholarly journals Collision and Stable Regions around Bodies with Simple Geometric Shape

2009 ◽  
Vol 2009 ◽  
pp. 1-14
Author(s):  
A. A. Silva ◽  
O. C. Winter ◽  
A. F. B. A. Prado
Keyword(s):  
Phase Space ◽  
Gravitational Potential ◽  
Geometric Shape ◽  
Irregular Surface ◽  
Geometric Shapes ◽  
Surface Of Section ◽  
Section Technique ◽  
Poincaré Surface Of Section ◽  
Simple Geometric Shape

We show the expressions of the gravitational potential of homogeneous bodies with well-defined simple geometric shapes to study the phase space of trajectories around these bodies. The potentials of the rectangular and triangular plates are presented. With these expressions we study the phase space of trajectories of a point of mass around the plates, using the Poincaré surface of section technique. We determined the location and the size of the stable and collision regions in the phase space, and the identification of some resonances. This work is the first and an important step for others studies, considering 3D bodies. The study of the behavior of a point of mass orbiting around these plates (2D), near their corners, can be used as a parameter to understand the influence of the gravitational potential when the particle is close to an irregular surface, such as large craters and ridges.

CHAOS IN ABELIAN AND NON-ABELIAN HIGGS SYSTEMS

1993 ◽  
Vol 08 (10) ◽  
pp. 1755-1772 ◽  
Author(s):  
B. DEY ◽  
C.N. KUMAR ◽  
A. SEN
Keyword(s):  
Phase Space ◽  
Equations Of Motion ◽  
Higgs Model ◽  
Time Dependent ◽  
Abelian Higgs Model ◽  
Surface Of Section ◽  
Yang Mills ◽  
Poincaré Surface Of Section ◽  
Chaotic Nature ◽  
Parameter Values

The nonintegrability and chaotic nature of the Yang-Mills Higgs systems are considered. We have studied the Abelian Higgs model and the SO(3) Georgi-Glashow model (non-Abelian Higgs model), which possess vortices and monopole solutions respectively. The Painlevé analysis of the corresponding time-dependent equations of motion shows that both systems are nonintegrable for all choices of the parameter values. The Poincare surface-of-section plot shows the presence of chaotic trajectories in the phase space at certain parameter values for both systems. The chaotic nature of the trajectories is also indicated by the computations of the Lyapunov exponents of the corresponding systems.

Newgrange — Science or Symbolizm

1994 ◽  
Vol 60 (1) ◽  
pp. 85-96 ◽  
Author(s):  
Andrew B. Powell
Keyword(s):  
Scientific Discourse ◽  
Geometric Shape ◽  
Mortuary Practices ◽  
Political Control ◽  
Spatial Relationships ◽  
Left And Right ◽  
Unit Of Length ◽  
Simple Geometric Shape

The Newgrange passage tomb is examined for evidence of ‘Neolithic science’. Claims that it incorporated an astronomical alignment, and was constructed using Pythagorean geometry and the megalithic yard are reviewed as are scientific interpretations of its art. A new analysis of the tomb's structure reveals that it was based on a simple geometric shape measurable by a 13.1 m unit of length. The locations of particular motifs and decorated surfaces are shown to conform to the spatial relationships evident in the tomb's form. These are defined in terms of oppositions between left and right, front and back, inside and outside, visible and hidden, as well as making reference to symbols found in the art of the neighbouring passage tomb at Knowth.These features are interpreted, not as evidence of a specificically scientific discourse in the Irish Neolithic, but as the elaboration of elements common to the passage tomb ritual discourse. Competition for political control, in the context of mortuary practices, resulted in the increasing formalization and rigid interpretation of passage tomb symbolizm, and the ritualization of new areas of knowledge.

CHAOTIC SCATTERING IN TIME-DEPENDENT HAMILTONIAN SYSTEMS

1991 ◽  
Vol 01 (03) ◽  
pp. 667-679 ◽  
Author(s):  
YING-CHENG LAI ◽  
CELSO GREBOGI
Keyword(s):  
Phase Space ◽  
Measure Zero ◽  
Invariant Set ◽  
Time Dependent ◽  
Invariant Sets ◽  
Physical Origin ◽  
Chaotic Scattering ◽  
Periodic Oscillations ◽  
Surface Of Section ◽  
Oscillating Potential

We consider the classical scattering of particles in a one-degree-of-freedom, time-dependent Hamiltonian system. We demonstrate that chaotic scattering can be induced by periodic oscillations in the position of the potential. We study the invariant sets on a surface of section for different amplitudes of the oscillating potential. It is found that for small amplitudes, the phase space consists of nonescaping KAM islands and an escaping set. The escaping set is made up of a nonhyperbolic set that gives rise to chaotic scattering and remains of KAM islands. For large amplitudes, the phase space contains a Lebesgue measure zero invariant set that gives rise to chaotic scattering. In this regime, we also discuss the physical origin of the Cantor set responsible for the chaotic scattering and calculate its fractal dimension.

scholarly journals On merging of resonant periodic orbits 4:3; 3:2 and 2:1 in Sun-Jupiter photo gravitational restricted three-body problem

2019 ◽  
Vol 7 (1) ◽  
pp. 17
Author(s):  
Prashant Kumar ◽  
Ram Krishan Sharma
Keyword(s):  
Periodic Orbits ◽  
Radiation Pressure ◽  
Body Problem ◽  
Solar Radiation Pressure ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Surface Of Section ◽  
Poincaré Surface Of Section ◽  
Frame Work ◽  
Three Body

We explore the merging of resonant periodic orbits in the frame work of planar circular restricted three body problem with the help of Poincaré surface of section. We have studied the effect of solar radiation pressure on 4:3, 3:2 and 2:1 periodic orbits. It is found that radiation pressure helps in merging these orbits (4:3 and 3.2 into 1:1 resonance and 2:1 into 1:1 resonance). At the time of merging these orbits become near-circular. The period and size of these orbits reduce with the increase in radiation pressure.  

scholarly journals Physical modeling of metamatereals on the basis of the flat spiral coil

2020 ◽  
Vol 6 (4) ◽  
pp. 18-30
Author(s):  
Z.R. Idiatullov ◽  
◽  
I.I. Ahmetov ◽  
M.M. Fatyhov ◽  
S.V. Spiridonov ◽  
...  
Keyword(s):  
Experimental Data ◽  
Transmission Coefficient ◽  
Physical Modeling ◽  
Geometric Shape ◽  
Spiral Coil ◽  
Geometric Shapes ◽  
Modeling Methods ◽  
Spiral Coils ◽  
Flat Spiral

In this work, the problems of physical modeling of metamaterials based on flat spiral coils with different geometric shapes were considered. The main parameters of the structures metamaterial modeling, methods of creation, as well as their unique properties are considered. As a result of physical modeling, structures were obtained that model the metamaterial with different values of dimensions and parameters. On the basis of the experimental data, the best variant of the geometric shape of the structure element was determined, based on the highest transmission coefficient.

GEOMETRIC SHAPE CONSTRUCTION IN WOMEN’S TRANSFORMING CLOTHING DESIGN

2016 ◽  
pp. 124
Author(s):  
Zelma Kackane
Keyword(s):  
Geometric Shape ◽  
Geometrical Shape ◽  
Fashion Industry ◽  
Geometric Shapes ◽  
Global Industry ◽  
Women's Clothing ◽  
Product Manufacturing ◽  
Material Utilization ◽  
Fashion Designers ◽  
User Friendly

Aim of the article – to analyze a geometric shape construction and transforming opportunities in women clothing design.This article studies and explains the Latgale national costume and modern high fashion applied the geometrical shape of women's clothing designs. Latvian national costumes are very important and nationally unique cultural heritage and they are divided into archaeological and ethnographic folk costumes. Nowadays, the fashion industry is a global industry that has the effect of the clothing and every season changing trends. It is used in a variety of shapes, occasionally repetitive fashion, or has become classics. The study shows that Latgale folk costume construction mainly consists of a rectangular geometric shapes and high fashion is used in similar design collection development. Latgale folk costume design consists of a rectangular geometric shapes where the fabric is made directly for the intended product, creating a 100% material utilization. As time has passed by national costume of the basic design has remained, but has evolved development methods and more user-friendly technology that facilitates product manufacturing and usage. Fashion designers create a certain time and place topical seasonal clothing patterns. There is a tendency to return to a more permissive cuts and drops in order to feel comfortable in any situation with an emphasis on garments function just as the ancestors of Latgale. 

scholarly journals On the Stability of Resonant Asteroid Orbits

1983 ◽  
Vol 74 ◽  
pp. 141-152 ◽  
Author(s):  
J.D. Hadjidemetriou ◽  
S. Ichtiaroglou
Keyword(s):  
Phase Space ◽  
Periodic Orbits ◽  
Energy Levels ◽  
The Other ◽  
Stable Region ◽  
Surface Of Section ◽  
Resonant Orbits ◽  
Symmetric Periodic Orbits ◽  
The Stability ◽  
Selection Of

AbstractThe stability of the asteroid orbits has been studied by the method of surface of section. Families of simple symmetric periodic orbits of the asteroid and their stability have been computed and this served as a guide for the selection of the energy levels for the surface of section. In this way all possible cases for the structure of phase space have been obtained. It was found that the region in phase space around the resonant orbits at the resonances 1/3, 3/5, 5/7,.... is unstable, but small stability regions of doubly symmetric periodic orbits near the above resonances are also present. At the resonances 1/2, 2/3, 3/4, .... it was found that there exist two separate regions in phase space at about the same resonance 1/2, 2/3, 3/4,...., respectively, one being stable and the other unstable. At certain energy levels only the stable region appears. The above results are consistent with the observed distribution of the asteroids.

scholarly journals APPLICATION OF DEPLOYABLE BAR STRUCTURES IN ARCHITECTURE: PROPOSAL FOR UNIVERSAL MULTIFUNCIONAL MODULE

2020 ◽  
Vol 8 (12) ◽  
pp. 817-826
Author(s):  
Amela Sljvic ◽  
◽  
Sladana Miljanovic ◽  
Muhamed Zlatar ◽  
◽  
...  
Keyword(s):  
Design Process ◽  
Geometric Shape ◽  
Transportation Costs ◽  
Healthcare Education ◽  
Temporary Housing ◽  
Lightweight Materials ◽  
Geometric Shapes ◽  
Architectural Structures ◽  
Doubly Curved ◽  
Functional Content

Deployable bar structures are made of lightweight materials, and that is one of the reason why they do not require high transportation costs, are easy to assemble (by unfolding) and disassemble (by folding) and are able to successfully respond to many requirements when in the shortest possible time it is necessary to provide architectural structures for various purposes. In this paper, the deployable bar structures are analyzed with the aim of forming a universal multifunctional space which could be used as a facility for temporary housing, healthcare, education and similar purposes. Due to the fact that geometric shape of a certain space significantly determines the function of that space, and the way it is used, detailed analyses of the geometric shapes of these structures have been conducted. Comparison of the forms explored so far with the existing architectural deployable bar structures has resulted in two distinct geometric forms: singly curved (barrel vault) and doubly curved (dome). It was concluded that the application of these forms in the form of freestanding modules provides limited opportunities for organizing functional content due to the specific locations of certain connections between elements, as well as the complicated design process. This is one of the reasons for rare application of these structures in architecture. The proposal of a multifunctional “Universal module 6” which consists of unified singly curved modules in combination with doubly curved and prismatic forms came as a result of the conducted analyses. Proposals for forming more complex architectural spaces of higher capacity provide a wider range of applications of these structures and opens new possibilities for their use.

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