Two-Dimensional Rigid-Body Collisions With Friction

1992 ◽  
Vol 59 (3) ◽  
pp. 635-642 ◽  
Author(s):  
Yu Wang ◽  
Matthew T. Mason
Keyword(s):  
Rigid Body ◽  
Graphical Method ◽  
Correct Identification ◽  
Two Dimensional ◽  
Contact Mode ◽  
New Class ◽  
Tangential Impact ◽  
Approach Velocity ◽  
Conservation Principles ◽  
Analytical Expressions

This paper presents an analysis of a two-dimensional rigid-body collision with dry friction. We use Routh’s graphical method to describe an impact process and to determine the frictional impulse. We classify the possible modes of impact, and derive analytical expressions for impulse, using both Poisson’s and Newton’s models of restitution. We also address a new class of impacts, tangential impact, with zero initial approach velocity. Some methods for rigid-body impact violate energy conservation principles, yielding solutions that increase system energy during an impact. To avoid such anomalies, we show that Poisson’s hypothesis should be used, rather than Newton’s law of restitution. In addition, correct identification of the contact mode of impact is essential.

New Methods for Analyzing Water Pollutants

1982 ◽  
Vol 14 (4-5) ◽  
pp. 59-71 ◽  
Author(s):  
L H Keith ◽  
R C Hall ◽  
R C Hanisch ◽  
R G Landolt ◽  
J E Henderson
Keyword(s):  
Amino Acids ◽  
Gas Chromatography ◽  
Two Dimensional ◽  
Gas Chromatograph ◽  
New Class ◽  
New Methods ◽  
System A ◽  
Drinking Waters ◽  
Computer Controlled ◽  
Nitrogen Containing Compounds

Two new methods have been developed to analyze for organic pollutants in water. The first, two-dimensional gas chromatography, using post detector peak recycling (PDPR), involves the use of a computer-controlled gas Chromatograph to selectively trap compounds of interest and rechromatograph them on a second column, recycling them through the same detector again. The second employs a new detector system, a thermally modulated electron capture detector (TMECD). Both methods were used to demonstrate their utility by applying them to the analysis of a new class of potentially ubiquitous anthropoaqueous pollutants in drinking waters- -haloacetonitriles. These newly identified compounds are produced from certain amino acids and other nitrogen-containing compounds reacting with chlorine during the disinfection stage of treatment.

CALCULATION OF THE DEPENDENCE OF THE DISTANCE TO THE LOCATED OBJECT FROM THE CORNER POSITION OF THE VEHICLE LINE

2018 ◽  
pp. 14-18
Author(s):  
V. V. Artyushenko ◽  
A. V. Nikulin
Keyword(s):  
Real Time ◽  
Statistical Physics ◽  
Angular Position ◽  
Three Dimensional ◽  
Line Of Sight ◽  
Two Dimensional ◽  
Radar Station ◽  
Flight Mode ◽  
Vector Algebra ◽  
Analytical Expressions

To simulate echoes from the earth’s surface in the low flight mode, it is necessary to reproduce reliably the delayed reflected sounding signal of the radar in real time. For this, it is necessary to be able to calculate accurately and quickly the dependence of the distance to the object being measured from the angular position of the line of sight of the radar station. Obviously, the simplest expressions for calculating the range can be obtained for a segment or a plane. In the text of the article, analytical expressions for the calculation of range for two-dimensional and three-dimensional cases are obtained. Methods of statistical physics, vector algebra, and the theory of the radar of extended objects were used. Since the calculation of the dependence of the range of the object to the target from the angular position of the line of sight is carried out on the analytical expressions found in the paper, the result obtained is accurate, and due to the relative simplicity of the expressions obtained, the calculation does not require much time.

scholarly journals Covalent assembly of a two-dimensional molecular “sponge” on a Cu(111) surface: confined electronic surface states in open and closed pores

2014 ◽  
Vol 50 (57) ◽  
pp. 7628-7631 ◽  
Author(s):  
Aneliia Shchyrba ◽  
Susanne C. Martens ◽  
Christian Wäckerlin ◽  
Manfred Matena ◽  
Toni Ivas ◽  
...  
Keyword(s):  
Surface States ◽  
Two Dimensional ◽  
New Class ◽  
Trimesic Acid ◽  
Electronic Surface

We present a new class of on-surface covalent reactions, formed between diborylene-3,4,9,10-tetraaminoperylene and trimesic acid on Cu(111), which gives rise to a porous 2D-‘sponge’.

scholarly journals Dielectric Function of a Quantum-Confined Thin Film with a Modified Pöschel–Teller Potential

2018 ◽  
Vol 63 (12) ◽  
pp. 1109 ◽  
Author(s):  
Kh. A. Gasanov ◽  
J. I. Guseinov ◽  
I. I. Abbasov ◽  
F. I. Mamedov ◽  
D. J. Askerov
Keyword(s):  
Dielectric Permittivity ◽  
Electron Gas ◽  
Two Dimensional ◽  
Quantum Nanostructures ◽  
Carrier Scattering ◽  
Scattering Potential ◽  
Quantum Confined ◽  
Charge Carrier Scattering ◽  
First Time ◽  
Analytical Expressions

The spatial and time dispersions of the dielectric permittivity of an electron gas in quasi-two-dimensional quantum nanostructures are studied. The screening of the charge-carrier scattering potential in a quantum-confined film with a modified P¨oschel–Teller potential is considered for the first time. Analytical expressions for the dielectric permittivity are obtained.

scholarly journals Frequency-Dependent Tensile and Compressive Effective Moduli of Elastic Solids With Randomly Distributed Two-Dimensional Microcracks

2015 ◽  
Vol 82 (8) ◽  
Author(s):  
Youxuan Zhao ◽  
Yanjun Qiu ◽  
Laurence J. Jacobs ◽  
Jianmin Qu
Keyword(s):  
Wave Attenuation ◽  
Two Dimensional ◽  
Effective Moduli ◽  
The Finite Element Method ◽  
Elastic Solids ◽  
Frequency Dependent ◽  
Micromechanics Models ◽  
Dynamic Case ◽  
Crack Faces ◽  
Analytical Expressions

This paper develops micromechanics models to estimate the tensile and compressive elastic moduli of elastic solids containing randomly distributed two-dimensional microcracks. The crack faces are open under tension and closed under compression. When the crack faces are closed, they may slide against one another following the Coulomb's law of dry friction. The micromechanics models provide analytical expressions of the tensile and compressive moduli for both static and dynamic cases. It is found that the tensile and compressive moduli are different. Further, under dynamic loading, the compressive and tensile moduli are both frequency dependent. As a by-product, the micromechanics models also predict wave attenuation in the dynamic case. Numerical simulations using the finite element method (FEM) are conducted to validate the micromechanics models.

UNBOUNDED SETS OF ATTRACTION

2000 ◽  
Vol 10 (06) ◽  
pp. 1437-1469 ◽  
Author(s):  
GIAN-ITALO BISCHI ◽  
CHRISTIAN MIRA ◽  
LAURA GARDINI
Keyword(s):  
Functional Equation ◽  
Two Dimensional ◽  
Elementary Functions ◽  
Theoretical Methods ◽  
One Dimensional ◽  
Zero Measure ◽  
Analytical Expressions

In this paper we show that unbounded chaotic trajectories are easily observed in the iteration of maps which are not defined everywhere, due to the presence of a denominator which vanishes in a zero-measure set. Through simple examples, obtained by the iteration of one-dimensional and two-dimensional maps with denominator, the basic mechanisms which are at the basis of the existence of unbounded chaotic trajectories are explained. Moreover, new kinds of contact bifurcations, which mark the transition from bounded to unbounded sets of attraction, are studied both through the examples and by general theoretical methods. Some of the maps studied in this paper have been obtained by a method based on the Schröoder functional equation, which allows one to write closed analytical expressions of the unbounded chaotic trajectories, in terms of elementary functions.

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